diff --git a/mypy/checker.py b/mypy/checker.py
index f3dc5d75f06d..97547b331a85 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -3353,15 +3353,18 @@ def find_isinstance_check(self, node: Expression
                             if isinstance(t, TypeType):
                                 union_list.append(t.item)
                             else:
-                                #  this is an error that should be reported earlier
-                                #  if we reach here, we refuse to do any type inference
+                                # This is an error that should be reported earlier
+                                # if we reach here, we refuse to do any type inference.
                                 return {}, {}
                         vartype = UnionType(union_list)
                     elif isinstance(vartype, TypeType):
                         vartype = vartype.item
+                    elif (isinstance(vartype, Instance) and
+                            vartype.type.fullname() == 'builtins.type'):
+                        vartype = self.named_type('builtins.object')
                     else:
-                        # any other object whose type we don't know precisely
-                        # for example, Any or Instance of type type
+                        # Any other object whose type we don't know precisely
+                        # for example, Any or a custom metaclass.
                         return {}, {}  # unknown type
                     yes_map, no_map = conditional_type_map(expr, vartype, type)
                     yes_map, no_map = map(convert_to_typetype, (yes_map, no_map))
@@ -3920,7 +3923,11 @@ def convert_to_typetype(type_map: TypeMap) -> TypeMap:
     if type_map is None:
         return None
     for expr, typ in type_map.items():
-        if not isinstance(typ, (UnionType, Instance)):
+        t = typ
+        if isinstance(t, TypeVarType):
+            t = t.upper_bound
+        # TODO: should we only allow unions of instances as per PEP 484?
+        if not isinstance(t, (UnionType, Instance)):
             # unknown type; error was likely reported earlier
             return {}
         converted_type_map[expr] = TypeType.make_normalized(typ)
diff --git a/mypy/meet.py b/mypy/meet.py
index 10d5b051293a..efab8744e82c 100644
--- a/mypy/meet.py
+++ b/mypy/meet.py
@@ -49,10 +49,10 @@ def narrow_declared_type(declared: Type, narrowed: Type) -> Type:
                                                 for x in narrowed.relevant_items()])
     elif isinstance(narrowed, AnyType):
         return narrowed
-    elif isinstance(declared, (Instance, TupleType)):
-        return meet_types(declared, narrowed)
     elif isinstance(declared, TypeType) and isinstance(narrowed, TypeType):
         return TypeType.make_normalized(narrow_declared_type(declared.item, narrowed.item))
+    elif isinstance(declared, (Instance, TupleType, TypeType)):
+        return meet_types(declared, narrowed)
     return narrowed
 
 
@@ -484,6 +484,12 @@ def visit_callable_type(self, t: CallableType) -> Type:
                 # Return a plain None or <uninhabited> instead of a weird function.
                 return self.default(self.s)
             return result
+        elif isinstance(self.s, TypeType) and t.is_type_obj() and not t.is_generic():
+            # In this case we are able to potentially produce a better meet.
+            res = meet_types(self.s.item, t.ret_type)
+            if not isinstance(res, (NoneTyp, UninhabitedType)):
+                return TypeType.make_normalized(res)
+            return self.default(self.s)
         elif isinstance(self.s, Instance) and self.s.type.is_protocol:
             call = unpack_callback_protocol(self.s)
             if call:
@@ -567,6 +573,8 @@ def visit_type_type(self, t: TypeType) -> Type:
             return typ
         elif isinstance(self.s, Instance) and self.s.type.fullname() == 'builtins.type':
             return t
+        elif isinstance(self.s, CallableType):
+            return self.meet(t, self.s)
         else:
             return self.default(self.s)
 
diff --git a/mypy/subtypes.py b/mypy/subtypes.py
index 83ebd468b9b3..d3886533eaeb 100644
--- a/mypy/subtypes.py
+++ b/mypy/subtypes.py
@@ -1193,7 +1193,6 @@ def visit_partial_type(self, left: PartialType) -> bool:
         return False
 
     def visit_type_type(self, left: TypeType) -> bool:
-        # TODO: Handle metaclasses?
         right = self.right
         if isinstance(right, TypeType):
             # This is unsound, we don't check the __init__ signature.
@@ -1210,6 +1209,12 @@ def visit_type_type(self, left: TypeType) -> bool:
                 return True
             if right.type.fullname() == 'builtins.object':
                 return True
+            item = left.item
+            if isinstance(item, TypeVarType):
+                item = item.upper_bound
+            if isinstance(item, Instance):
+                metaclass = item.type.metaclass_type
+                return metaclass is not None and self._is_proper_subtype(metaclass, right)
         return False
 
 
diff --git a/test-data/unit/check-classes.test b/test-data/unit/check-classes.test
index 6ee486935882..68cb74737392 100644
--- a/test-data/unit/check-classes.test
+++ b/test-data/unit/check-classes.test
@@ -5715,3 +5715,92 @@ class Test:
     def __init__(self) -> None:
         some_module = self.a
 [out]
+
+[case testIsInstanceTypeVsMetaclass]
+from typing import Type
+class Meta(type):
+    pass
+class Thing(metaclass=Meta):
+    pass
+
+def foo(x: Type[Thing]) -> Type[Thing]:
+    assert isinstance(x, Meta)
+    return x
+[builtins fixtures/isinstancelist.pyi]
+
+[case testIsInstanceTypeVsUnionOfType]
+from typing import Type, Union
+
+class AA: pass
+class AB: pass
+
+class M: pass
+
+class A(M, AA): pass
+class B(M, AB): pass
+
+AOrB = Union[A, B]
+
+class T(object):
+    def __init__(self, typ: Type[AOrB] = A) -> None:
+        assert isinstance(typ, type(M))
+        self.typ: Type[AOrB] = typ
+[builtins fixtures/isinstancelist.pyi]
+
+[case testIsInstanceTypeIsSubclass]
+from typing import Union, Type
+
+class C: ...
+
+x: Union[C, Type[C]]
+
+if isinstance(x, type) and issubclass(x, C):
+    reveal_type(x)  # E: Revealed type is 'Type[__main__.C]'
+[builtins fixtures/isinstancelist.pyi]
+
+[case testIsInstanceTypeByAssert]
+class A:
+    x = 42
+
+i: type = A
+assert issubclass(i, A)
+reveal_type(i.x)  # E: Revealed type is 'builtins.int'
+[builtins fixtures/isinstancelist.pyi]
+
+[case testIsInstanceTypeTypeVar]
+from typing import Type, TypeVar, Generic
+
+class Base: ...
+class Sub(Base): ...
+
+T = TypeVar('T', bound=Base)
+
+class C(Generic[T]):
+    def meth(self, cls: Type[T]) -> None:
+        if not issubclass(cls, Sub):
+            return
+        reveal_type(cls)  # E: Revealed type is 'Type[__main__.Sub]'
+    def other(self, cls: Type[T]) -> None:
+        if not issubclass(cls, Sub):
+            return
+        reveal_type(cls)  # E: Revealed type is 'Type[__main__.Sub]'
+
+[builtins fixtures/isinstancelist.pyi]
+
+[case testIsInstanceTypeSubclass]
+# flags: --strict-optional
+from typing import Type, Optional
+class Base: ...
+class One(Base): ...
+class Other(Base): ...
+
+def test() -> None:
+    x: Optional[Type[Base]]
+    if int():
+        x = One
+    elif int():
+        x = Other
+    else:
+        return
+    reveal_type(x)  # E: Revealed type is 'Union[Type[__main__.One], Type[__main__.Other]]'
+[builtins fixtures/isinstancelist.pyi]
diff --git a/test-data/unit/check-unions.test b/test-data/unit/check-unions.test
index da90bc6dcd2e..50c7b5260d33 100644
--- a/test-data/unit/check-unions.test
+++ b/test-data/unit/check-unions.test
@@ -410,8 +410,8 @@ def u(x: T, y: S) -> Union[S, T]: pass
 a: Any
 t_a: Type[A]
 
-reveal_type(u(M(*a), t_a)) # E: Revealed type is 'Union[Type[__main__.A], __main__.M*]'
-reveal_type(u(t_a, M(*a))) # E: Revealed type is 'Union[__main__.M*, Type[__main__.A]]'
+reveal_type(u(M(*a), t_a)) # E: Revealed type is '__main__.M*'
+reveal_type(u(t_a, M(*a))) # E: Revealed type is '__main__.M*'
 
 reveal_type(u(M2(*a), t_a)) # E: Revealed type is 'Union[Type[__main__.A], __main__.M2*]'
 reveal_type(u(t_a, M2(*a))) # E: Revealed type is 'Union[__main__.M2*, Type[__main__.A]]'