diff --git a/changelog.d/7976.misc b/changelog.d/7976.misc
new file mode 100644
index 000000000000..dfe4c03171d6
--- /dev/null
+++ b/changelog.d/7976.misc
@@ -0,0 +1 @@
+Convert various parts of the codebase to async/await.
diff --git a/synapse/storage/data_stores/main/event_push_actions.py b/synapse/storage/data_stores/main/event_push_actions.py
index 18297cf3b856..ad828389017b 100644
--- a/synapse/storage/data_stores/main/event_push_actions.py
+++ b/synapse/storage/data_stores/main/event_push_actions.py
@@ -15,11 +15,10 @@
 # limitations under the License.
 
 import logging
+from typing import List
 
 from canonicaljson import json
 
-from twisted.internet import defer
-
 from synapse.metrics.background_process_metrics import run_as_background_process
 from synapse.storage._base import LoggingTransaction, SQLBaseStore, db_to_json
 from synapse.storage.database import Database
@@ -166,8 +165,9 @@ def _get_unread_counts_by_pos_txn(self, txn, room_id, user_id, stream_ordering):
 
         return {"notify_count": notify_count, "highlight_count": highlight_count}
 
-    @defer.inlineCallbacks
-    def get_push_action_users_in_range(self, min_stream_ordering, max_stream_ordering):
+    async def get_push_action_users_in_range(
+        self, min_stream_ordering, max_stream_ordering
+    ):
         def f(txn):
             sql = (
                 "SELECT DISTINCT(user_id) FROM event_push_actions WHERE"
@@ -176,26 +176,28 @@ def f(txn):
             txn.execute(sql, (min_stream_ordering, max_stream_ordering))
             return [r[0] for r in txn]
 
-        ret = yield self.db.runInteraction("get_push_action_users_in_range", f)
+        ret = await self.db.runInteraction("get_push_action_users_in_range", f)
         return ret
 
-    @defer.inlineCallbacks
-    def get_unread_push_actions_for_user_in_range_for_http(
-        self, user_id, min_stream_ordering, max_stream_ordering, limit=20
-    ):
+    async def get_unread_push_actions_for_user_in_range_for_http(
+        self,
+        user_id: str,
+        min_stream_ordering: int,
+        max_stream_ordering: int,
+        limit: int = 20,
+    ) -> List[dict]:
         """Get a list of the most recent unread push actions for a given user,
         within the given stream ordering range. Called by the httppusher.
 
         Args:
-            user_id (str): The user to fetch push actions for.
-            min_stream_ordering(int): The exclusive lower bound on the
+            user_id: The user to fetch push actions for.
+            min_stream_ordering: The exclusive lower bound on the
                 stream ordering of event push actions to fetch.
-            max_stream_ordering(int): The inclusive upper bound on the
+            max_stream_ordering: The inclusive upper bound on the
                 stream ordering of event push actions to fetch.
-            limit (int): The maximum number of rows to return.
+            limit: The maximum number of rows to return.
         Returns:
-            A promise which resolves to a list of dicts with the keys "event_id",
-            "room_id", "stream_ordering", "actions".
+            A list of dicts with the keys "event_id", "room_id", "stream_ordering", "actions".
             The list will be ordered by ascending stream_ordering.
             The list will have between 0~limit entries.
         """
@@ -228,7 +230,7 @@ def get_after_receipt(txn):
             txn.execute(sql, args)
             return txn.fetchall()
 
-        after_read_receipt = yield self.db.runInteraction(
+        after_read_receipt = await self.db.runInteraction(
             "get_unread_push_actions_for_user_in_range_http_arr", get_after_receipt
         )
 
@@ -256,7 +258,7 @@ def get_no_receipt(txn):
             txn.execute(sql, args)
             return txn.fetchall()
 
-        no_read_receipt = yield self.db.runInteraction(
+        no_read_receipt = await self.db.runInteraction(
             "get_unread_push_actions_for_user_in_range_http_nrr", get_no_receipt
         )
 
@@ -280,23 +282,25 @@ def get_no_receipt(txn):
         # one of the subqueries may have hit the limit.
         return notifs[:limit]
 
-    @defer.inlineCallbacks
-    def get_unread_push_actions_for_user_in_range_for_email(
-        self, user_id, min_stream_ordering, max_stream_ordering, limit=20
-    ):
+    async def get_unread_push_actions_for_user_in_range_for_email(
+        self,
+        user_id: str,
+        min_stream_ordering: int,
+        max_stream_ordering: int,
+        limit: int = 20,
+    ) -> List[dict]:
         """Get a list of the most recent unread push actions for a given user,
         within the given stream ordering range. Called by the emailpusher
 
         Args:
-            user_id (str): The user to fetch push actions for.
-            min_stream_ordering(int): The exclusive lower bound on the
+            user_id: The user to fetch push actions for.
+            min_stream_ordering: The exclusive lower bound on the
                 stream ordering of event push actions to fetch.
-            max_stream_ordering(int): The inclusive upper bound on the
+            max_stream_ordering: The inclusive upper bound on the
                 stream ordering of event push actions to fetch.
-            limit (int): The maximum number of rows to return.
+            limit: The maximum number of rows to return.
         Returns:
-            A promise which resolves to a list of dicts with the keys "event_id",
-            "room_id", "stream_ordering", "actions", "received_ts".
+            A list of dicts with the keys "event_id", "room_id", "stream_ordering", "actions", "received_ts".
             The list will be ordered by descending received_ts.
             The list will have between 0~limit entries.
         """
@@ -328,7 +332,7 @@ def get_after_receipt(txn):
             txn.execute(sql, args)
             return txn.fetchall()
 
-        after_read_receipt = yield self.db.runInteraction(
+        after_read_receipt = await self.db.runInteraction(
             "get_unread_push_actions_for_user_in_range_email_arr", get_after_receipt
         )
 
@@ -356,7 +360,7 @@ def get_no_receipt(txn):
             txn.execute(sql, args)
             return txn.fetchall()
 
-        no_read_receipt = yield self.db.runInteraction(
+        no_read_receipt = await self.db.runInteraction(
             "get_unread_push_actions_for_user_in_range_email_nrr", get_no_receipt
         )
 
@@ -461,17 +465,13 @@ def _add_push_actions_to_staging_txn(txn):
             "add_push_actions_to_staging", _add_push_actions_to_staging_txn
         )
 
-    @defer.inlineCallbacks
-    def remove_push_actions_from_staging(self, event_id):
+    async def remove_push_actions_from_staging(self, event_id: str) -> None:
         """Called if we failed to persist the event to ensure that stale push
         actions don't build up in the DB
-
-        Args:
-            event_id (str)
         """
 
         try:
-            res = yield self.db.simple_delete(
+            res = await self.db.simple_delete(
                 table="event_push_actions_staging",
                 keyvalues={"event_id": event_id},
                 desc="remove_push_actions_from_staging",
@@ -606,8 +606,7 @@ def _find_first_stream_ordering_after_ts_txn(txn, ts):
 
         return range_end
 
-    @defer.inlineCallbacks
-    def get_time_of_last_push_action_before(self, stream_ordering):
+    async def get_time_of_last_push_action_before(self, stream_ordering):
         def f(txn):
             sql = (
                 "SELECT e.received_ts"
@@ -620,7 +619,7 @@ def f(txn):
             txn.execute(sql, (stream_ordering,))
             return txn.fetchone()
 
-        result = yield self.db.runInteraction("get_time_of_last_push_action_before", f)
+        result = await self.db.runInteraction("get_time_of_last_push_action_before", f)
         return result[0] if result else None
 
 
@@ -650,8 +649,7 @@ def __init__(self, database: Database, db_conn, hs):
             self._start_rotate_notifs, 30 * 60 * 1000
         )
 
-    @defer.inlineCallbacks
-    def get_push_actions_for_user(
+    async def get_push_actions_for_user(
         self, user_id, before=None, limit=50, only_highlight=False
     ):
         def f(txn):
@@ -682,18 +680,17 @@ def f(txn):
             txn.execute(sql, args)
             return self.db.cursor_to_dict(txn)
 
-        push_actions = yield self.db.runInteraction("get_push_actions_for_user", f)
+        push_actions = await self.db.runInteraction("get_push_actions_for_user", f)
         for pa in push_actions:
             pa["actions"] = _deserialize_action(pa["actions"], pa["highlight"])
         return push_actions
 
-    @defer.inlineCallbacks
-    def get_latest_push_action_stream_ordering(self):
+    async def get_latest_push_action_stream_ordering(self):
         def f(txn):
             txn.execute("SELECT MAX(stream_ordering) FROM event_push_actions")
             return txn.fetchone()
 
-        result = yield self.db.runInteraction(
+        result = await self.db.runInteraction(
             "get_latest_push_action_stream_ordering", f
         )
         return result[0] or 0
@@ -747,8 +744,7 @@ def _remove_old_push_actions_before_txn(
     def _start_rotate_notifs(self):
         return run_as_background_process("rotate_notifs", self._rotate_notifs)
 
-    @defer.inlineCallbacks
-    def _rotate_notifs(self):
+    async def _rotate_notifs(self):
         if self._doing_notif_rotation or self.stream_ordering_day_ago is None:
             return
         self._doing_notif_rotation = True
@@ -757,12 +753,12 @@ def _rotate_notifs(self):
             while True:
                 logger.info("Rotating notifications")
 
-                caught_up = yield self.db.runInteraction(
+                caught_up = await self.db.runInteraction(
                     "_rotate_notifs", self._rotate_notifs_txn
                 )
                 if caught_up:
                     break
-                yield self.hs.get_clock().sleep(self._rotate_delay)
+                await self.hs.get_clock().sleep(self._rotate_delay)
         finally:
             self._doing_notif_rotation = False
 
diff --git a/synapse/storage/data_stores/main/room.py b/synapse/storage/data_stores/main/room.py
index d2e1e36e7fb4..ab48052cdc9f 100644
--- a/synapse/storage/data_stores/main/room.py
+++ b/synapse/storage/data_stores/main/room.py
@@ -23,8 +23,6 @@
 
 from canonicaljson import json
 
-from twisted.internet import defer
-
 from synapse.api.constants import EventTypes
 from synapse.api.errors import StoreError
 from synapse.api.room_versions import RoomVersion, RoomVersions
@@ -32,7 +30,7 @@
 from synapse.storage.data_stores.main.search import SearchStore
 from synapse.storage.database import Database, LoggingTransaction
 from synapse.types import ThirdPartyInstanceID
-from synapse.util.caches.descriptors import cached, cachedInlineCallbacks
+from synapse.util.caches.descriptors import cached
 
 logger = logging.getLogger(__name__)
 
@@ -192,8 +190,7 @@ def _count_public_rooms_txn(txn):
 
         return self.db.runInteraction("count_public_rooms", _count_public_rooms_txn)
 
-    @defer.inlineCallbacks
-    def get_largest_public_rooms(
+    async def get_largest_public_rooms(
         self,
         network_tuple: Optional[ThirdPartyInstanceID],
         search_filter: Optional[dict],
@@ -330,10 +327,10 @@ def _get_largest_public_rooms_txn(txn):
 
             return results
 
-        ret_val = yield self.db.runInteraction(
+        ret_val = await self.db.runInteraction(
             "get_largest_public_rooms", _get_largest_public_rooms_txn
         )
-        defer.returnValue(ret_val)
+        return ret_val
 
     @cached(max_entries=10000)
     def is_room_blocked(self, room_id):
@@ -509,8 +506,8 @@ def _get_rooms_paginate_txn(txn):
             "get_rooms_paginate", _get_rooms_paginate_txn,
         )
 
-    @cachedInlineCallbacks(max_entries=10000)
-    def get_ratelimit_for_user(self, user_id):
+    @cached(max_entries=10000)
+    async def get_ratelimit_for_user(self, user_id):
         """Check if there are any overrides for ratelimiting for the given
         user
 
@@ -522,7 +519,7 @@ def get_ratelimit_for_user(self, user_id):
             of RatelimitOverride are None or 0 then ratelimitng has been
             disabled for that user entirely.
         """
-        row = yield self.db.simple_select_one(
+        row = await self.db.simple_select_one(
             table="ratelimit_override",
             keyvalues={"user_id": user_id},
             retcols=("messages_per_second", "burst_count"),
@@ -538,8 +535,8 @@ def get_ratelimit_for_user(self, user_id):
         else:
             return None
 
-    @cachedInlineCallbacks()
-    def get_retention_policy_for_room(self, room_id):
+    @cached()
+    async def get_retention_policy_for_room(self, room_id):
         """Get the retention policy for a given room.
 
         If no retention policy has been found for this room, returns a policy defined
@@ -566,19 +563,17 @@ def get_retention_policy_for_room_txn(txn):
 
             return self.db.cursor_to_dict(txn)
 
-        ret = yield self.db.runInteraction(
+        ret = await self.db.runInteraction(
             "get_retention_policy_for_room", get_retention_policy_for_room_txn,
         )
 
         # If we don't know this room ID, ret will be None, in this case return the default
         # policy.
         if not ret:
-            defer.returnValue(
-                {
-                    "min_lifetime": self.config.retention_default_min_lifetime,
-                    "max_lifetime": self.config.retention_default_max_lifetime,
-                }
-            )
+            return {
+                "min_lifetime": self.config.retention_default_min_lifetime,
+                "max_lifetime": self.config.retention_default_max_lifetime,
+            }
 
         row = ret[0]
 
@@ -592,7 +587,7 @@ def get_retention_policy_for_room_txn(txn):
         if row["max_lifetime"] is None:
             row["max_lifetime"] = self.config.retention_default_max_lifetime
 
-        defer.returnValue(row)
+        return row
 
     def get_media_mxcs_in_room(self, room_id):
         """Retrieves all the local and remote media MXC URIs in a given room
@@ -881,8 +876,7 @@ def __init__(self, database: Database, db_conn, hs):
             self._background_add_rooms_room_version_column,
         )
 
-    @defer.inlineCallbacks
-    def _background_insert_retention(self, progress, batch_size):
+    async def _background_insert_retention(self, progress, batch_size):
         """Retrieves a list of all rooms within a range and inserts an entry for each of
         them into the room_retention table.
         NULLs the property's columns if missing from the retention event in the room's
@@ -940,14 +934,14 @@ def _background_insert_retention_txn(txn):
             else:
                 return False
 
-        end = yield self.db.runInteraction(
+        end = await self.db.runInteraction(
             "insert_room_retention", _background_insert_retention_txn,
         )
 
         if end:
-            yield self.db.updates._end_background_update("insert_room_retention")
+            await self.db.updates._end_background_update("insert_room_retention")
 
-        defer.returnValue(batch_size)
+        return batch_size
 
     async def _background_add_rooms_room_version_column(
         self, progress: dict, batch_size: int
@@ -1096,8 +1090,7 @@ async def upsert_room_on_join(self, room_id: str, room_version: RoomVersion):
             lock=False,
         )
 
-    @defer.inlineCallbacks
-    def store_room(
+    async def store_room(
         self,
         room_id: str,
         room_creator_user_id: str,
@@ -1140,7 +1133,7 @@ def store_room_txn(txn, next_id):
                     )
 
             with self._public_room_id_gen.get_next() as next_id:
-                yield self.db.runInteraction("store_room_txn", store_room_txn, next_id)
+                await self.db.runInteraction("store_room_txn", store_room_txn, next_id)
         except Exception as e:
             logger.error("store_room with room_id=%s failed: %s", room_id, e)
             raise StoreError(500, "Problem creating room.")
@@ -1165,8 +1158,7 @@ async def maybe_store_room_on_invite(self, room_id: str, room_version: RoomVersi
             lock=False,
         )
 
-    @defer.inlineCallbacks
-    def set_room_is_public(self, room_id, is_public):
+    async def set_room_is_public(self, room_id, is_public):
         def set_room_is_public_txn(txn, next_id):
             self.db.simple_update_one_txn(
                 txn,
@@ -1206,13 +1198,12 @@ def set_room_is_public_txn(txn, next_id):
                 )
 
         with self._public_room_id_gen.get_next() as next_id:
-            yield self.db.runInteraction(
+            await self.db.runInteraction(
                 "set_room_is_public", set_room_is_public_txn, next_id
             )
         self.hs.get_notifier().on_new_replication_data()
 
-    @defer.inlineCallbacks
-    def set_room_is_public_appservice(
+    async def set_room_is_public_appservice(
         self, room_id, appservice_id, network_id, is_public
     ):
         """Edit the appservice/network specific public room list.
@@ -1287,7 +1278,7 @@ def set_room_is_public_appservice_txn(txn, next_id):
                 )
 
         with self._public_room_id_gen.get_next() as next_id:
-            yield self.db.runInteraction(
+            await self.db.runInteraction(
                 "set_room_is_public_appservice",
                 set_room_is_public_appservice_txn,
                 next_id,
@@ -1327,52 +1318,47 @@ def add_event_report(
     def get_current_public_room_stream_id(self):
         return self._public_room_id_gen.get_current_token()
 
-    @defer.inlineCallbacks
-    def block_room(self, room_id, user_id):
+    async def block_room(self, room_id: str, user_id: str) -> None:
         """Marks the room as blocked. Can be called multiple times.
 
         Args:
-            room_id (str): Room to block
-            user_id (str): Who blocked it
-
-        Returns:
-            Deferred
+            room_id: Room to block
+            user_id: Who blocked it
         """
-        yield self.db.simple_upsert(
+        await self.db.simple_upsert(
             table="blocked_rooms",
             keyvalues={"room_id": room_id},
             values={},
             insertion_values={"user_id": user_id},
             desc="block_room",
         )
-        yield self.db.runInteraction(
+        await self.db.runInteraction(
             "block_room_invalidation",
             self._invalidate_cache_and_stream,
             self.is_room_blocked,
             (room_id,),
         )
 
-    @defer.inlineCallbacks
-    def get_rooms_for_retention_period_in_range(
-        self, min_ms, max_ms, include_null=False
-    ):
+    async def get_rooms_for_retention_period_in_range(
+        self, min_ms: Optional[int], max_ms: Optional[int], include_null: bool = False
+    ) -> Dict[str, dict]:
         """Retrieves all of the rooms within the given retention range.
 
         Optionally includes the rooms which don't have a retention policy.
 
         Args:
-            min_ms (int|None): Duration in milliseconds that define the lower limit of
+            min_ms: Duration in milliseconds that define the lower limit of
                 the range to handle (exclusive). If None, doesn't set a lower limit.
-            max_ms (int|None): Duration in milliseconds that define the upper limit of
+            max_ms: Duration in milliseconds that define the upper limit of
                 the range to handle (inclusive). If None, doesn't set an upper limit.
-            include_null (bool): Whether to include rooms which retention policy is NULL
+            include_null: Whether to include rooms which retention policy is NULL
                 in the returned set.
 
         Returns:
-            dict[str, dict]: The rooms within this range, along with their retention
-                policy. The key is "room_id", and maps to a dict describing the retention
-                policy associated with this room ID. The keys for this nested dict are
-                "min_lifetime" (int|None), and "max_lifetime" (int|None).
+            The rooms within this range, along with their retention
+            policy. The key is "room_id", and maps to a dict describing the retention
+            policy associated with this room ID. The keys for this nested dict are
+            "min_lifetime" (int|None), and "max_lifetime" (int|None).
         """
 
         def get_rooms_for_retention_period_in_range_txn(txn):
@@ -1431,9 +1417,9 @@ def get_rooms_for_retention_period_in_range_txn(txn):
 
             return rooms_dict
 
-        rooms = yield self.db.runInteraction(
+        rooms = await self.db.runInteraction(
             "get_rooms_for_retention_period_in_range",
             get_rooms_for_retention_period_in_range_txn,
         )
 
-        defer.returnValue(rooms)
+        return rooms
diff --git a/synapse/storage/data_stores/main/state.py b/synapse/storage/data_stores/main/state.py
index bb38a04ede07..a36069940829 100644
--- a/synapse/storage/data_stores/main/state.py
+++ b/synapse/storage/data_stores/main/state.py
@@ -16,12 +16,12 @@
 import collections.abc
 import logging
 from collections import namedtuple
-
-from twisted.internet import defer
+from typing import Iterable, Optional, Set
 
 from synapse.api.constants import EventTypes, Membership
 from synapse.api.errors import NotFoundError, UnsupportedRoomVersionError
 from synapse.api.room_versions import KNOWN_ROOM_VERSIONS, RoomVersion
+from synapse.events import EventBase
 from synapse.storage._base import SQLBaseStore
 from synapse.storage.data_stores.main.events_worker import EventsWorkerStore
 from synapse.storage.data_stores.main.roommember import RoomMemberWorkerStore
@@ -108,28 +108,27 @@ async def get_room_version_id(self, room_id: str) -> str:
         create_event = await self.get_create_event_for_room(room_id)
         return create_event.content.get("room_version", "1")
 
-    @defer.inlineCallbacks
-    def get_room_predecessor(self, room_id):
+    async def get_room_predecessor(self, room_id: str) -> Optional[dict]:
         """Get the predecessor of an upgraded room if it exists.
         Otherwise return None.
 
         Args:
-            room_id (str)
+            room_id: The room ID.
 
         Returns:
-            Deferred[dict|None]: A dictionary containing the structure of the predecessor
-                field from the room's create event. The structure is subject to other servers,
-                but it is expected to be:
-                    * room_id (str): The room ID of the predecessor room
-                    * event_id (str): The ID of the tombstone event in the predecessor room
+            A dictionary containing the structure of the predecessor
+            field from the room's create event. The structure is subject to other servers,
+            but it is expected to be:
+                * room_id (str): The room ID of the predecessor room
+                * event_id (str): The ID of the tombstone event in the predecessor room
 
-                None if a predecessor key is not found, or is not a dictionary.
+            None if a predecessor key is not found, or is not a dictionary.
 
         Raises:
             NotFoundError if the given room is unknown
         """
         # Retrieve the room's create event
-        create_event = yield self.get_create_event_for_room(room_id)
+        create_event = await self.get_create_event_for_room(room_id)
 
         # Retrieve the predecessor key of the create event
         predecessor = create_event.content.get("predecessor", None)
@@ -140,20 +139,19 @@ def get_room_predecessor(self, room_id):
 
         return predecessor
 
-    @defer.inlineCallbacks
-    def get_create_event_for_room(self, room_id):
+    async def get_create_event_for_room(self, room_id: str) -> EventBase:
         """Get the create state event for a room.
 
         Args:
-            room_id (str)
+            room_id: The room ID.
 
         Returns:
-            Deferred[EventBase]: The room creation event.
+            The room creation event.
 
         Raises:
             NotFoundError if the room is unknown
         """
-        state_ids = yield self.get_current_state_ids(room_id)
+        state_ids = await self.get_current_state_ids(room_id)
         create_id = state_ids.get((EventTypes.Create, ""))
 
         # If we can't find the create event, assume we've hit a dead end
@@ -161,7 +159,7 @@ def get_create_event_for_room(self, room_id):
             raise NotFoundError("Unknown room %s" % (room_id,))
 
         # Retrieve the room's create event and return
-        create_event = yield self.get_event(create_id)
+        create_event = await self.get_event(create_id)
         return create_event
 
     @cached(max_entries=100000, iterable=True)
@@ -237,18 +235,17 @@ def _get_filtered_current_state_ids_txn(txn):
             "get_filtered_current_state_ids", _get_filtered_current_state_ids_txn
         )
 
-    @defer.inlineCallbacks
-    def get_canonical_alias_for_room(self, room_id):
+    async def get_canonical_alias_for_room(self, room_id: str) -> Optional[str]:
         """Get canonical alias for room, if any
 
         Args:
-            room_id (str)
+            room_id: The room ID
 
         Returns:
-            Deferred[str|None]: The canonical alias, if any
+            The canonical alias, if any
         """
 
-        state = yield self.get_filtered_current_state_ids(
+        state = await self.get_filtered_current_state_ids(
             room_id, StateFilter.from_types([(EventTypes.CanonicalAlias, "")])
         )
 
@@ -256,7 +253,7 @@ def get_canonical_alias_for_room(self, room_id):
         if not event_id:
             return
 
-        event = yield self.get_event(event_id, allow_none=True)
+        event = await self.get_event(event_id, allow_none=True)
         if not event:
             return
 
@@ -292,19 +289,19 @@ def _get_state_group_for_events(self, event_ids):
 
         return {row["event_id"]: row["state_group"] for row in rows}
 
-    @defer.inlineCallbacks
-    def get_referenced_state_groups(self, state_groups):
+    async def get_referenced_state_groups(
+        self, state_groups: Iterable[int]
+    ) -> Set[int]:
         """Check if the state groups are referenced by events.
 
         Args:
-            state_groups (Iterable[int])
+            state_groups
 
         Returns:
-            Deferred[set[int]]: The subset of state groups that are
-            referenced.
+            The subset of state groups that are referenced.
         """
 
-        rows = yield self.db.simple_select_many_batch(
+        rows = await self.db.simple_select_many_batch(
             table="event_to_state_groups",
             column="state_group",
             iterable=state_groups,
diff --git a/synapse/storage/data_stores/main/stats.py b/synapse/storage/data_stores/main/stats.py
index 380c1ec7dacc..922400a7c3be 100644
--- a/synapse/storage/data_stores/main/stats.py
+++ b/synapse/storage/data_stores/main/stats.py
@@ -16,8 +16,8 @@
 
 import logging
 from itertools import chain
+from typing import Tuple
 
-from twisted.internet import defer
 from twisted.internet.defer import DeferredLock
 
 from synapse.api.constants import EventTypes, Membership
@@ -97,13 +97,12 @@ def quantise_stats_time(self, ts):
         """
         return (ts // self.stats_bucket_size) * self.stats_bucket_size
 
-    @defer.inlineCallbacks
-    def _populate_stats_process_users(self, progress, batch_size):
+    async def _populate_stats_process_users(self, progress, batch_size):
         """
         This is a background update which regenerates statistics for users.
         """
         if not self.stats_enabled:
-            yield self.db.updates._end_background_update("populate_stats_process_users")
+            await self.db.updates._end_background_update("populate_stats_process_users")
             return 1
 
         last_user_id = progress.get("last_user_id", "")
@@ -118,20 +117,20 @@ def _get_next_batch(txn):
             txn.execute(sql, (last_user_id, batch_size))
             return [r for r, in txn]
 
-        users_to_work_on = yield self.db.runInteraction(
+        users_to_work_on = await self.db.runInteraction(
             "_populate_stats_process_users", _get_next_batch
         )
 
         # No more rooms -- complete the transaction.
         if not users_to_work_on:
-            yield self.db.updates._end_background_update("populate_stats_process_users")
+            await self.db.updates._end_background_update("populate_stats_process_users")
             return 1
 
         for user_id in users_to_work_on:
-            yield self._calculate_and_set_initial_state_for_user(user_id)
+            await self._calculate_and_set_initial_state_for_user(user_id)
             progress["last_user_id"] = user_id
 
-        yield self.db.runInteraction(
+        await self.db.runInteraction(
             "populate_stats_process_users",
             self.db.updates._background_update_progress_txn,
             "populate_stats_process_users",
@@ -140,13 +139,12 @@ def _get_next_batch(txn):
 
         return len(users_to_work_on)
 
-    @defer.inlineCallbacks
-    def _populate_stats_process_rooms(self, progress, batch_size):
+    async def _populate_stats_process_rooms(self, progress, batch_size):
         """
         This is a background update which regenerates statistics for rooms.
         """
         if not self.stats_enabled:
-            yield self.db.updates._end_background_update("populate_stats_process_rooms")
+            await self.db.updates._end_background_update("populate_stats_process_rooms")
             return 1
 
         last_room_id = progress.get("last_room_id", "")
@@ -161,20 +159,20 @@ def _get_next_batch(txn):
             txn.execute(sql, (last_room_id, batch_size))
             return [r for r, in txn]
 
-        rooms_to_work_on = yield self.db.runInteraction(
+        rooms_to_work_on = await self.db.runInteraction(
             "populate_stats_rooms_get_batch", _get_next_batch
         )
 
         # No more rooms -- complete the transaction.
         if not rooms_to_work_on:
-            yield self.db.updates._end_background_update("populate_stats_process_rooms")
+            await self.db.updates._end_background_update("populate_stats_process_rooms")
             return 1
 
         for room_id in rooms_to_work_on:
-            yield self._calculate_and_set_initial_state_for_room(room_id)
+            await self._calculate_and_set_initial_state_for_room(room_id)
             progress["last_room_id"] = room_id
 
-        yield self.db.runInteraction(
+        await self.db.runInteraction(
             "_populate_stats_process_rooms",
             self.db.updates._background_update_progress_txn,
             "populate_stats_process_rooms",
@@ -696,16 +694,16 @@ def get_changes_room_total_events_and_bytes_txn(self, txn, low_pos, high_pos):
 
         return room_deltas, user_deltas
 
-    @defer.inlineCallbacks
-    def _calculate_and_set_initial_state_for_room(self, room_id):
+    async def _calculate_and_set_initial_state_for_room(
+        self, room_id: str
+    ) -> Tuple[dict, dict, int]:
         """Calculate and insert an entry into room_stats_current.
 
         Args:
-            room_id (str)
+            room_id: The room ID under calculation.
 
         Returns:
-            Deferred[tuple[dict, dict, int]]: A tuple of room state, membership
-            counts and stream position.
+            A tuple of room state, membership counts and stream position.
         """
 
         def _fetch_current_state_stats(txn):
@@ -767,11 +765,11 @@ def _fetch_current_state_stats(txn):
             current_state_events_count,
             users_in_room,
             pos,
-        ) = yield self.db.runInteraction(
+        ) = await self.db.runInteraction(
             "get_initial_state_for_room", _fetch_current_state_stats
         )
 
-        state_event_map = yield self.get_events(event_ids, get_prev_content=False)
+        state_event_map = await self.get_events(event_ids, get_prev_content=False)
 
         room_state = {
             "join_rules": None,
@@ -806,11 +804,11 @@ def _fetch_current_state_stats(txn):
                     event.content.get("m.federate", True) is True
                 )
 
-        yield self.update_room_state(room_id, room_state)
+        await self.update_room_state(room_id, room_state)
 
         local_users_in_room = [u for u in users_in_room if self.hs.is_mine_id(u)]
 
-        yield self.update_stats_delta(
+        await self.update_stats_delta(
             ts=self.clock.time_msec(),
             stats_type="room",
             stats_id=room_id,
@@ -826,8 +824,7 @@ def _fetch_current_state_stats(txn):
             },
         )
 
-    @defer.inlineCallbacks
-    def _calculate_and_set_initial_state_for_user(self, user_id):
+    async def _calculate_and_set_initial_state_for_user(self, user_id):
         def _calculate_and_set_initial_state_for_user_txn(txn):
             pos = self._get_max_stream_id_in_current_state_deltas_txn(txn)
 
@@ -842,12 +839,12 @@ def _calculate_and_set_initial_state_for_user_txn(txn):
             (count,) = txn.fetchone()
             return count, pos
 
-        joined_rooms, pos = yield self.db.runInteraction(
+        joined_rooms, pos = await self.db.runInteraction(
             "calculate_and_set_initial_state_for_user",
             _calculate_and_set_initial_state_for_user_txn,
         )
 
-        yield self.update_stats_delta(
+        await self.update_stats_delta(
             ts=self.clock.time_msec(),
             stats_type="user",
             stats_id=user_id,
diff --git a/synapse/storage/data_stores/state/store.py b/synapse/storage/data_stores/state/store.py
index 128c09a2cffb..7dada7f75f83 100644
--- a/synapse/storage/data_stores/state/store.py
+++ b/synapse/storage/data_stores/state/store.py
@@ -139,10 +139,9 @@ def _get_state_group_delta_txn(txn):
             "get_state_group_delta", _get_state_group_delta_txn
         )
 
-    @defer.inlineCallbacks
-    def _get_state_groups_from_groups(
+    async def _get_state_groups_from_groups(
         self, groups: List[int], state_filter: StateFilter
-    ):
+    ) -> Dict[int, StateMap[str]]:
         """Returns the state groups for a given set of groups from the
         database, filtering on types of state events.
 
@@ -151,13 +150,13 @@ def _get_state_groups_from_groups(
             state_filter: The state filter used to fetch state
                 from the database.
         Returns:
-            Deferred[Dict[int, StateMap[str]]]: Dict of state group to state map.
+            Dict of state group to state map.
         """
         results = {}
 
         chunks = [groups[i : i + 100] for i in range(0, len(groups), 100)]
         for chunk in chunks:
-            res = yield self.db.runInteraction(
+            res = await self.db.runInteraction(
                 "_get_state_groups_from_groups",
                 self._get_state_groups_from_groups_txn,
                 chunk,
@@ -206,10 +205,9 @@ def _get_state_for_group_using_cache(self, cache, group, state_filter):
 
         return state_filter.filter_state(state_dict_ids), not missing_types
 
-    @defer.inlineCallbacks
-    def _get_state_for_groups(
+    async def _get_state_for_groups(
         self, groups: Iterable[int], state_filter: StateFilter = StateFilter.all()
-    ):
+    ) -> Dict[int, StateMap[str]]:
         """Gets the state at each of a list of state groups, optionally
         filtering by type/state_key
 
@@ -219,7 +217,7 @@ def _get_state_for_groups(
             state_filter: The state filter used to fetch state
                 from the database.
         Returns:
-            Deferred[Dict[int, StateMap[str]]]: Dict of state group to state map.
+            Dict of state group to state map.
         """
 
         member_filter, non_member_filter = state_filter.get_member_split()
@@ -228,14 +226,11 @@ def _get_state_for_groups(
         (
             non_member_state,
             incomplete_groups_nm,
-        ) = yield self._get_state_for_groups_using_cache(
+        ) = self._get_state_for_groups_using_cache(
             groups, self._state_group_cache, state_filter=non_member_filter
         )
 
-        (
-            member_state,
-            incomplete_groups_m,
-        ) = yield self._get_state_for_groups_using_cache(
+        (member_state, incomplete_groups_m,) = self._get_state_for_groups_using_cache(
             groups, self._state_group_members_cache, state_filter=member_filter
         )
 
@@ -256,7 +251,7 @@ def _get_state_for_groups(
         # Help the cache hit ratio by expanding the filter a bit
         db_state_filter = state_filter.return_expanded()
 
-        group_to_state_dict = yield self._get_state_groups_from_groups(
+        group_to_state_dict = await self._get_state_groups_from_groups(
             list(incomplete_groups), state_filter=db_state_filter
         )
 
@@ -576,19 +571,19 @@ def _purge_unreferenced_state_groups(self, txn, room_id, state_groups_to_delete)
             ((sg,) for sg in state_groups_to_delete),
         )
 
-    @defer.inlineCallbacks
-    def get_previous_state_groups(self, state_groups):
+    async def get_previous_state_groups(
+        self, state_groups: Iterable[int]
+    ) -> Dict[int, int]:
         """Fetch the previous groups of the given state groups.
 
         Args:
-            state_groups (Iterable[int])
+            state_groups
 
         Returns:
-            Deferred[dict[int, int]]: mapping from state group to previous
-            state group.
+            A mapping from state group to previous state group.
         """
 
-        rows = yield self.db.simple_select_many_batch(
+        rows = await self.db.simple_select_many_batch(
             table="state_group_edges",
             column="prev_state_group",
             iterable=state_groups,
diff --git a/synapse/storage/state.py b/synapse/storage/state.py
index 49ee9c9a7400..534883361fd7 100644
--- a/synapse/storage/state.py
+++ b/synapse/storage/state.py
@@ -14,7 +14,7 @@
 # limitations under the License.
 
 import logging
-from typing import Dict, Iterable, List, Optional, Set, Tuple, TypeVar
+from typing import Awaitable, Dict, Iterable, List, Optional, Set, Tuple, TypeVar
 
 import attr
 
@@ -419,7 +419,7 @@ async def get_state_groups(
 
     def _get_state_groups_from_groups(
         self, groups: List[int], state_filter: StateFilter
-    ):
+    ) -> Awaitable[Dict[int, StateMap[str]]]:
         """Returns the state groups for a given set of groups, filtering on
         types of state events.
 
@@ -429,7 +429,7 @@ def _get_state_groups_from_groups(
                 from the database.
 
         Returns:
-            Deferred[Dict[int, StateMap[str]]]: Dict of state group to state map.
+            Dict of state group to state map.
         """
 
         return self.stores.state._get_state_groups_from_groups(groups, state_filter)
@@ -532,7 +532,7 @@ async def get_state_ids_for_event(
 
     def _get_state_for_groups(
         self, groups: Iterable[int], state_filter: StateFilter = StateFilter.all()
-    ):
+    ) -> Awaitable[Dict[int, StateMap[str]]]:
         """Gets the state at each of a list of state groups, optionally
         filtering by type/state_key
 
@@ -540,8 +540,9 @@ def _get_state_for_groups(
             groups: list of state groups for which we want to get the state.
             state_filter: The state filter used to fetch state.
                 from the database.
+
         Returns:
-            Deferred[dict[int, StateMap[str]]]: Dict of state group to state map.
+            Dict of state group to state map.
         """
         return self.stores.state._get_state_for_groups(groups, state_filter)
 
diff --git a/tests/storage/test_event_push_actions.py b/tests/storage/test_event_push_actions.py
index 43dbeb42c598..2b1580feebaa 100644
--- a/tests/storage/test_event_push_actions.py
+++ b/tests/storage/test_event_push_actions.py
@@ -39,14 +39,18 @@ def setUp(self):
 
     @defer.inlineCallbacks
     def test_get_unread_push_actions_for_user_in_range_for_http(self):
-        yield self.store.get_unread_push_actions_for_user_in_range_for_http(
-            USER_ID, 0, 1000, 20
+        yield defer.ensureDeferred(
+            self.store.get_unread_push_actions_for_user_in_range_for_http(
+                USER_ID, 0, 1000, 20
+            )
         )
 
     @defer.inlineCallbacks
     def test_get_unread_push_actions_for_user_in_range_for_email(self):
-        yield self.store.get_unread_push_actions_for_user_in_range_for_email(
-            USER_ID, 0, 1000, 20
+        yield defer.ensureDeferred(
+            self.store.get_unread_push_actions_for_user_in_range_for_email(
+                USER_ID, 0, 1000, 20
+            )
         )
 
     @defer.inlineCallbacks
diff --git a/tests/storage/test_room.py b/tests/storage/test_room.py
index a5f250d4779e..d07b985a8e04 100644
--- a/tests/storage/test_room.py
+++ b/tests/storage/test_room.py
@@ -37,11 +37,13 @@ def setUp(self):
         self.alias = RoomAlias.from_string("#a-room-name:test")
         self.u_creator = UserID.from_string("@creator:test")
 
-        yield self.store.store_room(
-            self.room.to_string(),
-            room_creator_user_id=self.u_creator.to_string(),
-            is_public=True,
-            room_version=RoomVersions.V1,
+        yield defer.ensureDeferred(
+            self.store.store_room(
+                self.room.to_string(),
+                room_creator_user_id=self.u_creator.to_string(),
+                is_public=True,
+                room_version=RoomVersions.V1,
+            )
         )
 
     @defer.inlineCallbacks
@@ -88,11 +90,13 @@ def setUp(self):
 
         self.room = RoomID.from_string("!abcde:test")
 
-        yield self.store.store_room(
-            self.room.to_string(),
-            room_creator_user_id="@creator:text",
-            is_public=True,
-            room_version=RoomVersions.V1,
+        yield defer.ensureDeferred(
+            self.store.store_room(
+                self.room.to_string(),
+                room_creator_user_id="@creator:text",
+                is_public=True,
+                room_version=RoomVersions.V1,
+            )
         )
 
     @defer.inlineCallbacks
diff --git a/tests/storage/test_state.py b/tests/storage/test_state.py
index 6a48b9d3b3a9..8bd12fa84723 100644
--- a/tests/storage/test_state.py
+++ b/tests/storage/test_state.py
@@ -44,11 +44,13 @@ def setUp(self):
 
         self.room = RoomID.from_string("!abc123:test")
 
-        yield self.store.store_room(
-            self.room.to_string(),
-            room_creator_user_id="@creator:text",
-            is_public=True,
-            room_version=RoomVersions.V1,
+        yield defer.ensureDeferred(
+            self.store.store_room(
+                self.room.to_string(),
+                room_creator_user_id="@creator:text",
+                is_public=True,
+                room_version=RoomVersions.V1,
+            )
         )
 
     @defer.inlineCallbacks