diff --git a/jedi/evaluate/pep0484.py b/jedi/evaluate/pep0484.py
index 422ca85f..8b4381ff 100644
--- a/jedi/evaluate/pep0484.py
+++ b/jedi/evaluate/pep0484.py
@@ -110,6 +110,13 @@ def get_types_for_typing_module(evaluator, typ, node):
         nodes = node.children[::2]  # skip the commas
     else:
         nodes = [node]
+    del node
+
+    # hacked in Union and Optional, since it's hard to do nicely in parsed code
+    if typ.name.value == "Union":
+        return set().union(*[evaluator.eval_element(node) for node in nodes])
+    if typ.name.value == "Optional":
+        return evaluator.eval_element(nodes[0])
 
     typing = _get_typing_replacement_module()
     factories = evaluator.find_types(typing, "factory")
diff --git a/test/completion/pep0484_typing.py b/test/completion/pep0484_typing.py
index 8b8ad852..6b085fc2 100644
--- a/test/completion/pep0484_typing.py
+++ b/test/completion/pep0484_typing.py
@@ -154,5 +154,32 @@ def mapping(
         ##? Value()  --- TODO fix support for tuple assignment
         value
 
+def union(
+        p: typing.Union[int],
+        q: typing.Union[int, int],
+        r: typing.Union[int, str, "int"],
+        s: typing.Union[int, typing.Union[str, "typing.Union['float', 'dict']"]],
+        t: typing.Union[int, None]):
+    #? int()
+    p
+    #? int()
+    q
+    #? int() str()
+    r
+    #? int() str() float() dict()
+    s
+    #? int()
+    t
+
+def optional(
+        p: typing.Optional[int]):
+    """
+    Optional does not do anything special. However it should be recognised
+    as being of that type. Jedi doesn't do anything with the extra into that
+    it can be None as well
+    """
+    #? int()
+    p
+
 class ForwardReference:
     pass