diff --git a/jedi/evaluate/iterable.py b/jedi/evaluate/iterable.py
index b11b95a1..5b0871fd 100644
--- a/jedi/evaluate/iterable.py
+++ b/jedi/evaluate/iterable.py
@@ -29,6 +29,7 @@ from jedi.evaluate import compiled
 from jedi.evaluate import helpers
 from jedi.evaluate.cache import CachedMetaClass, memoize_default
 from jedi.evaluate import analysis
+from jedi.evaluate import pep0484
 
 
 class IterableWrapper(tree.Base):
@@ -560,12 +561,23 @@ def py__iter__types(evaluator, types, node=None):
 
 
 def py__getitem__(evaluator, types, index, node):
+    from jedi.evaluate.representation import Class
     result = set()
 
     # Index handling.
     if isinstance(index, (compiled.CompiledObject, Slice)):
         index = index.obj
 
+    # special case: PEP0484 typing module, see
+    # https://github.com/davidhalter/jedi/issues/663
+    for typ in list(types):
+        if isinstance(typ, Class):
+            replacementclass = \
+                pep0484.get_typing_replacement_class(evaluator, typ)
+            if replacementclass:
+                types.remove(typ)
+                result |= replacementclass.py__getitem__(index)
+
     if type(index) not in (float, int, str, unicode, slice):
         # If the index is not clearly defined, we have to get all the
         # possiblities.
@@ -588,7 +600,7 @@ def py__getitem__(evaluator, types, index, node):
             except IndexError:
                 result |= py__iter__types(evaluator, set([typ]))
             except KeyError:
-                # Must be a dict. Lists don't raise IndexErrors.
+                # Must be a dict. Lists don't raise KeyErrors.
                 result |= typ.dict_values()
     return result
 
diff --git a/jedi/evaluate/pep0484.py b/jedi/evaluate/pep0484.py
index 4eec2fed..761886a4 100644
--- a/jedi/evaluate/pep0484.py
+++ b/jedi/evaluate/pep0484.py
@@ -20,9 +20,10 @@ x support for type hint comments `# type: (int, str) -> int`. See comment from
 
 from itertools import chain
 
-from jedi.parser import Parser, load_grammar, ParseError
+from jedi.parser import Parser, load_grammar, ParseError, tree, ParserWithRecovery
 from jedi.evaluate.cache import memoize_default
-from jedi.evaluate.compiled import CompiledObject
+from jedi.evaluate import compiled
+from textwrap import dedent
 from jedi import debug
 
 
@@ -30,7 +31,7 @@ def _evaluate_for_annotation(evaluator, annotation):
     if annotation is not None:
         definitions = set()
         for definition in evaluator.eval_element(annotation):
-            if (isinstance(definition, CompiledObject) and
+            if (isinstance(definition, compiled.CompiledObject) and
                     isinstance(definition.obj, str)):
                 try:
                     p = Parser(load_grammar(), definition.obj, start='eval_input')
@@ -60,3 +61,40 @@ def follow_param(evaluator, param):
 def find_return_types(evaluator, func):
     annotation = func.py__annotations__().get("return", None)
     return _evaluate_for_annotation(evaluator, annotation)
+
+
+# TODO: Memoize
+def get_typing_replacement_module():
+    """
+    The idea is to return our jedi replacement for the PEP-0484 typing module
+    as discussed at https://github.com/davidhalter/jedi/issues/663
+    """
+
+    code = dedent("""
+    from collections import abc
+
+    class MakeSequence:
+        def __getitem__(self, indextype):
+            class Sequence(abc.Sequence):
+                def __getitem__(self) -> indextype:
+                    pass
+            return Sequence
+    """)
+    p = ParserWithRecovery(load_grammar(), code)
+    return p.module
+
+
+def get_typing_replacement_class(evaluator, typ):
+    if not typ.base.get_parent_until(tree.Module).name.value == "typing":
+        return None
+    # we assume that any class using [] in a module called
+    # "typing" with a name for which we have a replacement
+    # should be replaced by that class. This is not 100%
+    # airtight but I don't have a better idea to check that it's
+    # actually the PEP-0484 typing module and not some other
+    typing = get_typing_replacement_module()
+    types = evaluator.find_types(typing, "Make" + typ.name.value)
+    if not types:
+        return None
+    else:
+        return list(types)[0]
diff --git a/jedi/evaluate/representation.py b/jedi/evaluate/representation.py
index c460efd2..35359dbd 100644
--- a/jedi/evaluate/representation.py
+++ b/jedi/evaluate/representation.py
@@ -469,6 +469,24 @@ class Class(use_metaclass(CachedMetaClass, Wrapper)):
     def py__class__(self):
         return compiled.create(self._evaluator, type)
 
+    def py__getitem__(self, index):
+        instances = self.py__call__(())
+        assert len(instances) == 1
+        instance = list(instances)[0]
+        try:
+            method = instance.get_subscope_by_name('__getitem__')
+        except KeyError:
+            debug.warning('No __getitem__, cannot access the array.')
+            return set()
+        else:
+            # it feels like this should be handled somewhere else,
+            # not sure where though
+            if isinstance(index, type(self)):
+                index_obj = index
+            else:
+                index_obj = compiled.create(self._evaluator, index)
+            return instance._evaluator.execute_evaluated(method, index_obj)
+
     @property
     def params(self):
         return self.get_subscope_by_name('__init__').params
diff --git a/test/completion/pep0484.py b/test/completion/pep0484.py
index fc08460f..ba9044bc 100644
--- a/test/completion/pep0484.py
+++ b/test/completion/pep0484.py
@@ -157,3 +157,26 @@ Y = int
 def just_because_we_can(x: "flo" + "at"):
     #? float()
     x
+
+import typing
+def we_can_has_sequence(
+        p: typing.Sequence[int],
+        q: typing.Sequence[B],
+        r: "typing.Sequence[int]",
+        s: typing.Sequence["int"]):
+    #? ["count"]
+    p.c
+    #? int()
+    p[1]
+    #? ["count"]
+    q.c
+    #? B()
+    q[1]
+    #? ["count"]
+    r.c
+    #? int()
+    r[1]
+    #? ["count"]
+    s.c
+    #? int()
+    s[1]