diff --git a/jedi/inference/compiled/access.py b/jedi/inference/compiled/access.py
index 350db95a..dfca7d9c 100644
--- a/jedi/inference/compiled/access.py
+++ b/jedi/inference/compiled/access.py
@@ -484,6 +484,19 @@ class DirectObjectAccess(object):
         op = _OPERATORS[operator]
         return self._create_access_path(op(self._obj, other_access._obj))
 
+    def get_annotation_name_and_args(self):
+        """
+        Returns Tuple[Optional[str], Tuple[AccessPath, ...]]
+        """
+        if sys.version_info < (3, 5):
+            return None, ()
+
+        import typing
+        args = typing.get_args(self._obj)
+        origin = typing.get_origin(self._obj)
+        name = None if origin is None else str(origin)
+        return name, tuple(self._create_access_path(arg) for arg in args)
+
     def needs_type_completions(self):
         return inspect.isclass(self._obj) and self._obj != type
 
diff --git a/jedi/inference/compiled/value.py b/jedi/inference/compiled/value.py
index 3a54289e..54814294 100644
--- a/jedi/inference/compiled/value.py
+++ b/jedi/inference/compiled/value.py
@@ -271,6 +271,11 @@ class CompiledObject(Value):
         if self.access_handle.get_repr() == 'None':
             # None as an annotation doesn't need to be executed.
             return ValueSet([self])
+
+        name, args = self.access_handle.get_annotation_name_and_args()
+        arguments = [create_from_access_path(self.inference_state, path) for path in args]
+        if name == 'typing.Union':
+            return ValueSet.from_sets(arg.execute_annotation() for arg in arguments)
         return super(CompiledObject, self).execute_annotation()
 
     def negate(self):
diff --git a/test/test_api/test_interpreter.py b/test/test_api/test_interpreter.py
index 2c7a39e5..639a0e64 100644
--- a/test/test_api/test_interpreter.py
+++ b/test/test_api/test_interpreter.py
@@ -653,7 +653,11 @@ def bar():
         ({'return': 'foo()'}, []),
         ({'return': 'bar()'}, ['float']),
         # typing is available via globals.
-        #({'return': 'typing.Union[str, int]'}, ['str']),
+        ({'return': 'typing.Union[str, int]'}, ['int', 'str']),
+        ({'return': 'typing.Union["str", int]'}, ['int']),
+        ({'return': 'typing.Union["str", 1]'}, []),
+        ({'return': 'typing.Optional[str]'}, ['NoneType', 'str']),
+        ({'return': 'typing.Optional[str, int]'}, []),  # Takes only one arg
 
         ({'return': 'decimal.Decimal'}, []),
         ({'return': 'lalalalallalaa'}, []),