diff --git a/changelog.d/8505.misc b/changelog.d/8505.misc
new file mode 100644
index 000000000000..5aa5c113bd78
--- /dev/null
+++ b/changelog.d/8505.misc
@@ -0,0 +1 @@
+Add type hints to various parts of the code base.
diff --git a/mypy.ini b/mypy.ini
index a7ffb81ef133..19b60f7534d7 100644
--- a/mypy.ini
+++ b/mypy.ini
@@ -15,9 +15,12 @@ files =
   synapse/events/builder.py,
   synapse/events/spamcheck.py,
   synapse/federation,
+  synapse/handlers/account_data.py,
   synapse/handlers/auth.py,
   synapse/handlers/cas_handler.py,
+  synapse/handlers/deactivate_account.py,
   synapse/handlers/device.py,
+  synapse/handlers/devicemessage.py,
   synapse/handlers/directory.py,
   synapse/handlers/events.py,
   synapse/handlers/federation.py,
@@ -26,7 +29,9 @@ files =
   synapse/handlers/message.py,
   synapse/handlers/oidc_handler.py,
   synapse/handlers/pagination.py,
+  synapse/handlers/password_policy.py,
   synapse/handlers/presence.py,
+  synapse/handlers/read_marker.py,
   synapse/handlers/room.py,
   synapse/handlers/room_member.py,
   synapse/handlers/room_member_worker.py,
diff --git a/synapse/federation/federation_server.py b/synapse/federation/federation_server.py
index 02f11e120997..1c7ea886c9d4 100644
--- a/synapse/federation/federation_server.py
+++ b/synapse/federation/federation_server.py
@@ -861,7 +861,7 @@ def __init__(self, hs: "HomeServer"):
         self._edu_type_to_instance = {}  # type: Dict[str, str]
 
     def register_edu_handler(
-        self, edu_type: str, handler: Callable[[str, dict], Awaitable[None]]
+        self, edu_type: str, handler: Callable[[str, JsonDict], Awaitable[None]]
     ):
         """Sets the handler callable that will be used to handle an incoming
         federation EDU of the given type.
diff --git a/synapse/handlers/account_data.py b/synapse/handlers/account_data.py
index 9112a0ab8610..341135822eb9 100644
--- a/synapse/handlers/account_data.py
+++ b/synapse/handlers/account_data.py
@@ -12,16 +12,24 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+from typing import TYPE_CHECKING, List, Tuple
+
+from synapse.types import JsonDict, UserID
+
+if TYPE_CHECKING:
+    from synapse.app.homeserver import HomeServer
 
 
 class AccountDataEventSource:
-    def __init__(self, hs):
+    def __init__(self, hs: "HomeServer"):
         self.store = hs.get_datastore()
 
-    def get_current_key(self, direction="f"):
+    def get_current_key(self, direction: str = "f") -> int:
         return self.store.get_max_account_data_stream_id()
 
-    async def get_new_events(self, user, from_key, **kwargs):
+    async def get_new_events(
+        self, user: UserID, from_key: int, **kwargs
+    ) -> Tuple[List[JsonDict], int]:
         user_id = user.to_string()
         last_stream_id = from_key
 
diff --git a/synapse/handlers/deactivate_account.py b/synapse/handlers/deactivate_account.py
index 0635ad570866..72a583153187 100644
--- a/synapse/handlers/deactivate_account.py
+++ b/synapse/handlers/deactivate_account.py
@@ -14,7 +14,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 import logging
-from typing import Optional
+from typing import TYPE_CHECKING, Optional
 
 from synapse.api.errors import SynapseError
 from synapse.metrics.background_process_metrics import run_as_background_process
@@ -22,13 +22,16 @@
 
 from ._base import BaseHandler
 
+if TYPE_CHECKING:
+    from synapse.app.homeserver import HomeServer
+
 logger = logging.getLogger(__name__)
 
 
 class DeactivateAccountHandler(BaseHandler):
     """Handler which deals with deactivating user accounts."""
 
-    def __init__(self, hs):
+    def __init__(self, hs: "HomeServer"):
         super().__init__(hs)
         self.hs = hs
         self._auth_handler = hs.get_auth_handler()
@@ -137,7 +140,7 @@ async def deactivate_account(
 
         return identity_server_supports_unbinding
 
-    async def _reject_pending_invites_for_user(self, user_id: str):
+    async def _reject_pending_invites_for_user(self, user_id: str) -> None:
         """Reject pending invites addressed to a given user ID.
 
         Args:
diff --git a/synapse/handlers/devicemessage.py b/synapse/handlers/devicemessage.py
index 64ef7f63ab79..9cac5a846396 100644
--- a/synapse/handlers/devicemessage.py
+++ b/synapse/handlers/devicemessage.py
@@ -14,7 +14,7 @@
 # limitations under the License.
 
 import logging
-from typing import Any, Dict
+from typing import TYPE_CHECKING, Any, Dict
 
 from synapse.api.errors import SynapseError
 from synapse.logging.context import run_in_background
@@ -24,18 +24,22 @@
     set_tag,
     start_active_span,
 )
-from synapse.types import UserID, get_domain_from_id
+from synapse.types import JsonDict, UserID, get_domain_from_id
 from synapse.util import json_encoder
 from synapse.util.stringutils import random_string
 
+if TYPE_CHECKING:
+    from synapse.app.homeserver import HomeServer
+
+
 logger = logging.getLogger(__name__)
 
 
 class DeviceMessageHandler:
-    def __init__(self, hs):
+    def __init__(self, hs: "HomeServer"):
         """
         Args:
-            hs (synapse.server.HomeServer): server
+            hs: server
         """
         self.store = hs.get_datastore()
         self.notifier = hs.get_notifier()
@@ -48,7 +52,7 @@ def __init__(self, hs):
 
         self._device_list_updater = hs.get_device_handler().device_list_updater
 
-    async def on_direct_to_device_edu(self, origin, content):
+    async def on_direct_to_device_edu(self, origin: str, content: JsonDict) -> None:
         local_messages = {}
         sender_user_id = content["sender"]
         if origin != get_domain_from_id(sender_user_id):
@@ -95,7 +99,7 @@ async def _check_for_unknown_devices(
         message_type: str,
         sender_user_id: str,
         by_device: Dict[str, Dict[str, Any]],
-    ):
+    ) -> None:
         """Checks inbound device messages for unknown remote devices, and if
         found marks the remote cache for the user as stale.
         """
@@ -138,11 +142,16 @@ async def _check_for_unknown_devices(
                 self._device_list_updater.user_device_resync, sender_user_id
             )
 
-    async def send_device_message(self, sender_user_id, message_type, messages):
+    async def send_device_message(
+        self,
+        sender_user_id: str,
+        message_type: str,
+        messages: Dict[str, Dict[str, JsonDict]],
+    ) -> None:
         set_tag("number_of_messages", len(messages))
         set_tag("sender", sender_user_id)
         local_messages = {}
-        remote_messages = {}
+        remote_messages = {}  # type: Dict[str, Dict[str, Dict[str, JsonDict]]]
         for user_id, by_device in messages.items():
             # we use UserID.from_string to catch invalid user ids
             if self.is_mine(UserID.from_string(user_id)):
diff --git a/synapse/handlers/password_policy.py b/synapse/handlers/password_policy.py
index 88e2f8720058..6c635cc31b7e 100644
--- a/synapse/handlers/password_policy.py
+++ b/synapse/handlers/password_policy.py
@@ -16,14 +16,18 @@
 
 import logging
 import re
+from typing import TYPE_CHECKING
 
 from synapse.api.errors import Codes, PasswordRefusedError
 
+if TYPE_CHECKING:
+    from synapse.app.homeserver import HomeServer
+
 logger = logging.getLogger(__name__)
 
 
 class PasswordPolicyHandler:
-    def __init__(self, hs):
+    def __init__(self, hs: "HomeServer"):
         self.policy = hs.config.password_policy
         self.enabled = hs.config.password_policy_enabled
 
@@ -33,11 +37,11 @@ def __init__(self, hs):
         self.regexp_uppercase = re.compile("[A-Z]")
         self.regexp_lowercase = re.compile("[a-z]")
 
-    def validate_password(self, password):
+    def validate_password(self, password: str) -> None:
         """Checks whether a given password complies with the server's policy.
 
         Args:
-            password (str): The password to check against the server's policy.
+            password: The password to check against the server's policy.
 
         Raises:
             PasswordRefusedError: The password doesn't comply with the server's policy.
diff --git a/synapse/handlers/read_marker.py b/synapse/handlers/read_marker.py
index c32f314a1c0e..a7550806e6c4 100644
--- a/synapse/handlers/read_marker.py
+++ b/synapse/handlers/read_marker.py
@@ -14,23 +14,29 @@
 # limitations under the License.
 
 import logging
+from typing import TYPE_CHECKING
 
 from synapse.util.async_helpers import Linearizer
 
 from ._base import BaseHandler
 
+if TYPE_CHECKING:
+    from synapse.app.homeserver import HomeServer
+
 logger = logging.getLogger(__name__)
 
 
 class ReadMarkerHandler(BaseHandler):
-    def __init__(self, hs):
+    def __init__(self, hs: "HomeServer"):
         super().__init__(hs)
         self.server_name = hs.config.server_name
         self.store = hs.get_datastore()
         self.read_marker_linearizer = Linearizer(name="read_marker")
         self.notifier = hs.get_notifier()
 
-    async def received_client_read_marker(self, room_id, user_id, event_id):
+    async def received_client_read_marker(
+        self, room_id: str, user_id: str, event_id: str
+    ) -> None:
         """Updates the read marker for a given user in a given room if the event ID given
         is ahead in the stream relative to the current read marker.
 
diff --git a/synapse/notifier.py b/synapse/notifier.py
index 59415f6f88c5..13adeed01e5e 100644
--- a/synapse/notifier.py
+++ b/synapse/notifier.py
@@ -339,7 +339,7 @@ def on_new_event(
         self,
         stream_key: str,
         new_token: Union[int, RoomStreamToken],
-        users: Collection[UserID] = [],
+        users: Collection[Union[str, UserID]] = [],
         rooms: Collection[str] = [],
     ):
         """ Used to inform listeners that something has happened event wise.
diff --git a/synapse/storage/databases/main/registration.py b/synapse/storage/databases/main/registration.py
index a85867936f06..7fd7b0b952ca 100644
--- a/synapse/storage/databases/main/registration.py
+++ b/synapse/storage/databases/main/registration.py
@@ -1220,7 +1220,9 @@ async def record_user_external_id(
             desc="record_user_external_id",
         )
 
-    async def user_set_password_hash(self, user_id: str, password_hash: str) -> None:
+    async def user_set_password_hash(
+        self, user_id: str, password_hash: Optional[str]
+    ) -> None:
         """
         NB. This does *not* evict any cache because the one use for this
             removes most of the entries subsequently anyway so it would be