diff --git a/mypy/checker.py b/mypy/checker.py
index 229c1f087228..16bbc1c982a6 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -2643,6 +2643,9 @@ def visit_assignment_stmt(self, s: AssignmentStmt) -> None:
         ):
             self.fail(message_registry.DEPENDENT_FINAL_IN_CLASS_BODY, s)
 
+        if s.unanalyzed_type and not self.in_checked_function():
+            self.msg.annotation_in_unchecked_function(context=s)
+
     def check_type_alias_rvalue(self, s: AssignmentStmt) -> None:
         if not (self.is_stub and isinstance(s.rvalue, OpExpr) and s.rvalue.op == "|"):
             # We do this mostly for compatibility with old semantic analyzer.
diff --git a/mypy/errorcodes.py b/mypy/errorcodes.py
index 0d6a328693d4..fd0ee619a47d 100644
--- a/mypy/errorcodes.py
+++ b/mypy/errorcodes.py
@@ -137,6 +137,9 @@ def __str__(self) -> str:
 UNREACHABLE: Final = ErrorCode(
     "unreachable", "Warn about unreachable statements or expressions", "General"
 )
+ANNOTATION_UNCHECKED = ErrorCode(
+    "annotation-unchecked", "Notify about type annotations in unchecked functions", "General"
+)
 PARTIALLY_DEFINED: Final[ErrorCode] = ErrorCode(
     "partially-defined",
     "Warn about variables that are defined only in some execution paths",
diff --git a/mypy/messages.py b/mypy/messages.py
index f3aa1898bfd8..75e5134d1242 100644
--- a/mypy/messages.py
+++ b/mypy/messages.py
@@ -2148,6 +2148,14 @@ def add_fixture_note(self, fullname: str, ctx: Context) -> None:
                 ctx,
             )
 
+    def annotation_in_unchecked_function(self, context: Context) -> None:
+        self.note(
+            "By default the bodies of untyped functions are not checked,"
+            " consider using --check-untyped-defs",
+            context,
+            code=codes.ANNOTATION_UNCHECKED,
+        )
+
 
 def quote_type_string(type_string: str) -> str:
     """Quotes a type representation for use in messages."""
diff --git a/test-data/unit/check-classes.test b/test-data/unit/check-classes.test
index ae7d02f9edfc..b16387f194d4 100644
--- a/test-data/unit/check-classes.test
+++ b/test-data/unit/check-classes.test
@@ -1189,7 +1189,7 @@ reveal_type(Foo().Meta.name)  # N: Revealed type is "builtins.str"
 
 class A:
     def __init__(self):
-        self.x = None # type: int
+        self.x = None # type: int  # N: By default the bodies of untyped functions are not checked, consider using --check-untyped-defs
 a = None # type: A
 a.x = 1
 a.x = '' # E: Incompatible types in assignment (expression has type "str", variable has type "int")
@@ -1201,7 +1201,7 @@ a.x = 1
 a.x = '' # E: Incompatible types in assignment (expression has type "str", variable has type "int")
 class A:
     def __init__(self):
-        self.x = None # type: int
+        self.x = None # type: int  # N: By default the bodies of untyped functions are not checked, consider using --check-untyped-defs
 
 
 -- Special cases
diff --git a/test-data/unit/check-dataclasses.test b/test-data/unit/check-dataclasses.test
index 4b2ff1af2151..3ec4c60e6929 100644
--- a/test-data/unit/check-dataclasses.test
+++ b/test-data/unit/check-dataclasses.test
@@ -1641,7 +1641,7 @@ A(a=func).a = func  # E: Property "a" defined in "A" is read-only
 # flags: --python-version 3.7
 from dataclasses import dataclass
 
-def foo():
+def foo() -> None:
     @dataclass
     class Foo:
         foo: int
diff --git a/test-data/unit/check-errorcodes.test b/test-data/unit/check-errorcodes.test
index 4cd8e58f037d..ceae45956069 100644
--- a/test-data/unit/check-errorcodes.test
+++ b/test-data/unit/check-errorcodes.test
@@ -964,3 +964,8 @@ class C(abc.ABC):
 T = TypeVar("T")
 def test(tp: Type[T]) -> T: ...
 test(C)  # E: Only concrete class can be given where "Type[C]" is expected  [type-abstract]
+
+[case testUncheckedAnnotationSuppressed]
+# flags: --disable-error-code=annotation-unchecked
+def f():
+    x: int = "no"  # No warning here
diff --git a/test-data/unit/check-incremental.test b/test-data/unit/check-incremental.test
index ac005001b135..b258c57b961c 100644
--- a/test-data/unit/check-incremental.test
+++ b/test-data/unit/check-incremental.test
@@ -3544,11 +3544,11 @@ class Bar(Baz): pass
 
 [file c.py]
 class Baz:
-    def __init__(self):
+    def __init__(self) -> None:
         self.x = 12  # type: int
 [file c.py.2]
 class Baz:
-    def __init__(self):
+    def __init__(self) -> None:
         self.x = 'lol'  # type: str
 [out]
 [out2]
@@ -5730,6 +5730,7 @@ class C:
 tmp/a.py:2: error: "object" has no attribute "xyz"
 
 [case testIncrementalInvalidNamedTupleInUnannotatedFunction]
+# flags: --disable-error-code=annotation-unchecked
 import a
 
 [file a.py]
diff --git a/test-data/unit/check-inference-context.test b/test-data/unit/check-inference-context.test
index 3bab79f5aec2..2e26f54c6e93 100644
--- a/test-data/unit/check-inference-context.test
+++ b/test-data/unit/check-inference-context.test
@@ -814,7 +814,7 @@ if int():
 from typing import List
 class A:
   def __init__(self):
-    self.x = [] # type: List[int]
+    self.x = [] # type: List[int]  # N: By default the bodies of untyped functions are not checked, consider using --check-untyped-defs
 a = A()
 a.x = []
 a.x = [1]
diff --git a/test-data/unit/check-newsemanal.test b/test-data/unit/check-newsemanal.test
index a52be03e31ce..97cf1ef1494d 100644
--- a/test-data/unit/check-newsemanal.test
+++ b/test-data/unit/check-newsemanal.test
@@ -2963,6 +2963,7 @@ def g() -> None:
     reveal_type(y)  # N: Revealed type is "__main__.G[Any]"
 
 [case testNewAnalyzerRedefinedNonlocal]
+# flags: --disable-error-code=annotation-unchecked
 import typing
 
 def f():
@@ -2977,7 +2978,7 @@ def g() -> None:
 
     def foo() -> None:
         nonlocal bar
-        bar = []  # type: typing.List[int] # E: Name "bar" already defined on line 11
+        bar = []  # type: typing.List[int] # E: Name "bar" already defined on line 12
 [builtins fixtures/list.pyi]
 
 [case testNewAnalyzerMoreInvalidTypeVarArgumentsDeferred]
diff --git a/test-data/unit/check-statements.test b/test-data/unit/check-statements.test
index 9b571cb20c0d..4be5060996e2 100644
--- a/test-data/unit/check-statements.test
+++ b/test-data/unit/check-statements.test
@@ -2186,7 +2186,7 @@ N = TypedDict('N', {'x': int})
 [out]
 
 [case testGlobalWithoutInitialization]
-
+# flags: --disable-error-code=annotation-unchecked
 from typing import List
 
 def foo() -> None:
@@ -2200,3 +2200,9 @@ def foo2():
     bar2 = []  # type: List[str]
     bar2
 [builtins fixtures/list.pyi]
+
+[case testNoteUncheckedAnnotation]
+def foo():
+    x: int = "no"  # N: By default the bodies of untyped functions are not checked, consider using --check-untyped-defs
+    y = "no"  # type: int  # N: By default the bodies of untyped functions are not checked, consider using --check-untyped-defs
+    z: int  # N: By default the bodies of untyped functions are not checked, consider using --check-untyped-defs