diff --git a/mypy/stubtest.py b/mypy/stubtest.py
index f48d0ff05ffe..138f126c9d1a 100644
--- a/mypy/stubtest.py
+++ b/mypy/stubtest.py
@@ -858,8 +858,31 @@ def verify_decorator(
 def verify_typealias(
     stub: nodes.TypeAlias, runtime: MaybeMissing[Any], object_path: List[str]
 ) -> Iterator[Error]:
-    if False:
-        yield None
+    if isinstance(runtime, Missing):
+        # ignore type aliases that don't have a runtime counterpart
+        return
+    stub_target = mypy.types.get_proper_type(stub.target)
+    if isinstance(stub_target, mypy.types.Instance):
+        yield from verify(stub_target.type, runtime, object_path)
+        return
+    if isinstance(stub_target, mypy.types.UnionType):
+        if not getattr(runtime, "__origin__", None) is Union:
+            yield Error(object_path, "is not a Union", stub, runtime, stub_desc=str(stub_target))
+        # could check Union contents here...
+        return
+    if isinstance(stub_target, mypy.types.TupleType):
+        if tuple not in getattr(runtime, "__mro__", ()):
+            yield Error(
+                object_path, "is not a subclass of tuple", stub, runtime,
+                stub_desc=str(stub_target)
+            )
+        # could check Tuple contents here...
+        return
+    if isinstance(stub_target, mypy.types.AnyType):
+        return
+    yield Error(
+        object_path, "is not a recognised type alias", stub, runtime, stub_desc=str(stub_target)
+    )
 
 
 SPECIAL_DUNDERS = ("__init__", "__new__", "__call__", "__init_subclass__", "__class_getitem__")
@@ -887,10 +910,11 @@ def is_probably_a_function(runtime: Any) -> bool:
 def safe_inspect_signature(runtime: Any) -> Optional[inspect.Signature]:
     try:
         return inspect.signature(runtime)
-    except (ValueError, RuntimeError, TypeError):
-        # inspect.signature throws sometimes
+    except Exception:
+        # inspect.signature throws ValueError all the time
         # catch RuntimeError because of https://bugs.python.org/issue39504
         # catch TypeError because of https://github.com/python/typeshed/pull/5762
+        # catch AttributeError because of inspect.signature(_curses.window.border)
         return None
 
 
diff --git a/mypy/test/teststubtest.py b/mypy/test/teststubtest.py
index 0ce5df00aafd..7275037a9246 100644
--- a/mypy/test/teststubtest.py
+++ b/mypy/test/teststubtest.py
@@ -571,6 +571,30 @@ def __init__(self):
             error=None,
         )
 
+    @collect_cases
+    def test_type_alias(self) -> Iterator[Case]:
+        yield Case(
+            stub="""
+            class X:
+                def f(self) -> None: ...
+            Y = X
+            """,
+            runtime="""
+            class X:
+                def f(self) -> None: ...
+            class Y: ...
+            """,
+            error="Y.f",
+        )
+        yield Case(
+            stub="""
+            from typing import Tuple
+            A = Tuple[int, str]
+            """,
+            runtime="A = (int, str)",
+            error="A",
+        )
+
     @collect_cases
     def test_enum(self) -> Iterator[Case]:
         yield Case(