diff --git a/mypy/checker.py b/mypy/checker.py
index dc744c6d3467..7a131abb37be 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -877,8 +877,10 @@ def check_func_def(self, defn: FuncItem, typ: CallableType, name: Optional[str])
                 # Store argument types.
                 for i in range(len(typ.arg_types)):
                     arg_type = typ.arg_types[i]
-
-                    ref_type = self.scope.active_self_type()  # type: Optional[Type]
+                    with self.scope.push_function(defn):
+                        # We temporary push the definition to get the self type as
+                        # visible from *inside* of this function/method.
+                        ref_type = self.scope.active_self_type()  # type: Optional[Type]
                     if (isinstance(defn, FuncDef) and ref_type is not None and i == 0
                             and not defn.is_static
                             and typ.arg_kinds[0] not in [nodes.ARG_STAR, nodes.ARG_STAR2]):
@@ -4456,6 +4458,7 @@ def active_class(self) -> Optional[TypeInfo]:
         return None
 
     def enclosing_class(self) -> Optional[TypeInfo]:
+        """Is there a class *directly* enclosing this function?"""
         top = self.top_function()
         assert top, "This method must be called from inside a function"
         index = self.stack.index(top)
@@ -4466,7 +4469,14 @@ def enclosing_class(self) -> Optional[TypeInfo]:
         return None
 
     def active_self_type(self) -> Optional[Union[Instance, TupleType]]:
+        """An instance or tuple type representing the current class.
+
+        This returns None unless we are in class body or in a method.
+        In particular, inside a function nested in method this returns None.
+        """
         info = self.active_class()
+        if not info and self.top_function():
+            info = self.enclosing_class()
         if info:
             return fill_typevars(info)
         return None
diff --git a/test-data/unit/check-classes.test b/test-data/unit/check-classes.test
index 9a113ace0df1..bfe057e1de02 100644
--- a/test-data/unit/check-classes.test
+++ b/test-data/unit/check-classes.test
@@ -6077,3 +6077,68 @@ TX = TypeVar('TX', bound='X')
 class X:
     def __new__(cls, x: TX) -> TX:  # E: "__new__" must return a class instance (got "TX")
         pass
+
+[case testGenericOverride]
+from typing import Generic, TypeVar, Any
+
+T = TypeVar('T')
+
+class B(Generic[T]):
+    x: T
+
+class C(B):
+    def __init__(self) -> None:
+        self.x: Any
+
+[case testGenericOverridePreciseInvalid]
+from typing import Generic, TypeVar, Any
+
+T = TypeVar('T')
+
+class B(Generic[T]):
+    x: T
+
+class C(B[str]):
+    def __init__(self) -> None:
+        self.x: int  # E: Incompatible types in assignment (expression has type "int", base class "B" defined the type as "str")
+
+[case testGenericOverridePreciseValid]
+from typing import Generic, TypeVar
+
+T = TypeVar('T')
+
+class B(Generic[T]):
+    x: T
+
+class C(B[float]):
+    def __init__(self) -> None:
+        self.x: int  # We currently allow covariant overriding.
+
+[case testGenericOverrideGeneric]
+from typing import Generic, TypeVar, List
+
+T = TypeVar('T')
+
+class B(Generic[T]):
+    x: T
+
+class C(B[T]):
+    def __init__(self) -> None:
+        self.x: List[T]  # E: Incompatible types in assignment (expression has type "List[T]", base class "B" defined the type as "T")
+[builtins fixtures/list.pyi]
+
+[case testGenericOverrideGenericChained]
+from typing import Generic, TypeVar, Tuple
+
+T = TypeVar('T')
+S = TypeVar('S')
+
+class A(Generic[T]):
+    x: T
+
+class B(A[Tuple[T, S]]): ...
+
+class C(B[int, T]):
+    def __init__(self) -> None:
+        # TODO: error message could be better.
+        self.x: Tuple[str, T]  # E: Incompatible types in assignment (expression has type "Tuple[str, T]", base class "A" defined the type as "Tuple[int, T]")