diff --git a/.travis.yml b/.travis.yml
index b7e3d1211..47d42d6fd 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -6,12 +6,29 @@ python:
     - 3.4
     - 3.3
     - 2.7
+    - pypy
 sudo: false
 before_install:
     - git clone --quiet --depth 1 https://github.com/minrk/travis-wheels travis-wheels
     - 'if [[ $GROUP != js* ]]; then COVERAGE=""; fi'
 install:
     - pip install "setuptools>=18.5"
+    # Installs PyPy (+ its Numpy). Based on @frol comment at:
+    # https://github.com/travis-ci/travis-ci/issues/5027
+    - |
+        if [ "$TRAVIS_PYTHON_VERSION" = "pypy" ]; then
+          export PYENV_ROOT="$HOME/.pyenv"
+          if [ -f "$PYENV_ROOT/bin/pyenv" ]; then
+            cd "$PYENV_ROOT" && git pull
+          else
+            rm -rf "$PYENV_ROOT" && git clone --depth 1 https://github.com/yyuu/pyenv.git "$PYENV_ROOT"
+          fi
+          export PYPY_VERSION="5.3.1"
+          "$PYENV_ROOT/bin/pyenv" install "pypy-$PYPY_VERSION"
+          virtualenv --python="$PYENV_ROOT/versions/pypy-$PYPY_VERSION/bin/python" "$HOME/virtualenvs/pypy-$PYPY_VERSION"
+          source "$HOME/virtualenvs/pypy-$PYPY_VERSION/bin/activate"
+          pip install https://bitbucket.org/pypy/numpy/get/master.zip
+        fi
     - pip install -f travis-wheels/wheelhouse -e file://$PWD#egg=ipython[test]
     - pip install codecov
 script:
@@ -23,4 +40,5 @@ after_success:
 
 matrix:
     allow_failures:
-        python: nightly
+        - python: nightly
+        - python: pypy
diff --git a/IPython/core/completer.py b/IPython/core/completer.py
index 07bbbaa17..87b13b1c5 100644
--- a/IPython/core/completer.py
+++ b/IPython/core/completer.py
@@ -216,7 +216,11 @@ def completions_sorting_key(word):
 class Bunch(object): pass
 
 
-DELIMS = ' \t\n`!@#$^&*()=+[{]}\\|;:\'",<>?'
+if sys.platform == 'win32':
+    DELIMS = ' \t\n`!@#$^&*()=+[{]}|;\'",<>?'
+else:
+    DELIMS = ' \t\n`!@#$^&*()=+[{]}\\|;:\'",<>?'
+
 GREEDY_DELIMS = ' =\r\n'
 
 
@@ -729,7 +733,10 @@ def file_matches(self, text):
             return [text_prefix + cast_unicode_py2(protect_filename(f)) for f in self.glob("*")]
 
         # Compute the matches from the filesystem
-        m0 = self.clean_glob(text.replace('\\',''))
+        if sys.platform == 'win32':
+            m0 = self.clean_glob(text)
+        else:
+            m0 = self.clean_glob(text.replace('\\', ''))
 
         if has_protectables:
             # If we had protectables, we need to revert our changes to the
diff --git a/IPython/lib/pretty.py b/IPython/lib/pretty.py
index 49ee2cef3..97529f193 100644
--- a/IPython/lib/pretty.py
+++ b/IPython/lib/pretty.py
@@ -85,7 +85,7 @@ def _repr_pretty_(self, p, cycle):
 import datetime
 from collections import deque
 
-from IPython.utils.py3compat import PY3, cast_unicode, string_types
+from IPython.utils.py3compat import PY3, PYPY, cast_unicode, string_types
 from IPython.utils.encoding import get_stream_enc
 
 from io import StringIO
@@ -605,7 +605,8 @@ def inner(obj, p, cycle):
 
         if cycle:
             return p.text('{...}')
-        p.begin_group(1, start)
+        step = len(start)
+        p.begin_group(step, start)
         keys = obj.keys()
         # if dict isn't large enough to be truncated, sort keys before displaying
         if not (p.max_seq_length and len(obj) >= p.max_seq_length):
@@ -621,7 +622,7 @@ def inner(obj, p, cycle):
             p.pretty(key)
             p.text(': ')
             p.pretty(obj[key])
-        p.end_group(1, end)
+        p.end_group(step, end)
     return inner
 
 
@@ -631,7 +632,11 @@ def _super_pprint(obj, p, cycle):
     p.pretty(obj.__thisclass__)
     p.text(',')
     p.breakable()
-    p.pretty(obj.__self__)
+    if PYPY: # In PyPy, super() objects don't have __self__ attributes
+        dself = obj.__repr__.__self__
+        p.pretty(None if dself is obj else dself)
+    else:
+        p.pretty(obj.__self__)
     p.end_group(8, '>')
 
 
@@ -665,8 +670,10 @@ def _type_pprint(obj, p, cycle):
     # Heap allocated types might not have the module attribute,
     # and others may set it to None.
 
-    # Checks for a __repr__ override in the metaclass
-    if type(obj).__repr__ is not type.__repr__:
+    # Checks for a __repr__ override in the metaclass. Can't compare the
+    # type(obj).__repr__ directly because in PyPy the representation function
+    # inherited from type isn't the same type.__repr__
+    if [m for m in _get_mro(type(obj)) if "__repr__" in vars(m)][:1] != [type]:
         _repr_pprint(obj, p, cycle)
         return
 
@@ -753,10 +760,15 @@ def _exception_pprint(obj, p, cycle):
 }
 
 try:
-    _type_pprinters[types.DictProxyType] = _dict_pprinter_factory('<dictproxy {', '}>')
+    # In PyPy, types.DictProxyType is dict, setting the dictproxy printer
+    # using dict.setdefault avoids overwritting the dict printer
+    _type_pprinters.setdefault(types.DictProxyType,
+                               _dict_pprinter_factory('dict_proxy({', '})'))
     _type_pprinters[types.ClassType] = _type_pprint
     _type_pprinters[types.SliceType] = _repr_pprint
 except AttributeError: # Python 3
+    _type_pprinters[types.MappingProxyType] = \
+        _dict_pprinter_factory('mappingproxy({', '})')
     _type_pprinters[slice] = _repr_pprint
     
 try:
diff --git a/IPython/terminal/pt_inputhooks/tk.py b/IPython/terminal/pt_inputhooks/tk.py
index 24313a839..db205b0d2 100644
--- a/IPython/terminal/pt_inputhooks/tk.py
+++ b/IPython/terminal/pt_inputhooks/tk.py
@@ -40,10 +40,12 @@
 """
 import time
 
+from IPython.utils.py3compat import PY3
+
 import _tkinter
-try:
+if PY3:
     import tkinter
-except ImportError:
+else:
     import Tkinter as tkinter  # Python 2
 
 def inputhook(inputhook_context):
diff --git a/IPython/utils/py3compat.py b/IPython/utils/py3compat.py
index f42f55c95..88602e534 100644
--- a/IPython/utils/py3compat.py
+++ b/IPython/utils/py3compat.py
@@ -6,6 +6,7 @@
 import re
 import shutil
 import types
+import platform
 
 from .encoding import DEFAULT_ENCODING
 
@@ -292,6 +293,7 @@ def execfile(fname, glob=None, loc=None, compiler=None):
 
 
 PY2 = not PY3
+PYPY = platform.python_implementation() == "PyPy"
 
 
 def annotate(**kwargs):
diff --git a/tox.ini b/tox.ini
index 3a197386d..1668ce6f3 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,44 +1,28 @@
-# Tox (http://tox.testrun.org/) is a tool for running tests
-# in multiple virtualenvs. This configuration file will run the
-# test suite on all supported python versions. To use it, "pip install tox"
-# and then run "tox" from this directory.
-
-# Building the source distribution requires `invoke` and `lessc` to be on your PATH.
-# "pip install invoke" will install invoke. Less can be installed by
-# node.js' (http://nodejs.org/) package manager npm:
-# "npm install -g less".
-
-# Javascript tests need additional dependencies that can be installed
-# using node.js' package manager npm:
-# [*] casperjs:  "npm install -g casperjs"
-# [*] slimerjs:  "npm install -g slimerjs"
-# [*] phantomjs: "npm install -g phantomjs"
-
-# Note: qt4 versions break some tests with tornado versions >=4.0.
+; Tox (http://tox.testrun.org/) is a virtualenv manager for running tests in
+; multiple environments. This configuration file gets the requirements from
+; setup.py like a "pip install ipython[test]". To create the environments, it
+; requires every interpreter available/installed.
+;  -- Commands --
+; pip install tox  # Installs tox
+; tox              # Runs the tests (call from the directory with tox.ini)
+; tox -r           # Ditto, but forcing the virtual environments to be rebuilt
+; tox -e py35,pypy # Runs only in the selected environments
+; tox -- --all -j  # Runs "iptest --all -j" in every environment
 
 [tox]
-envlist = py27, py33, py34
+envlist = py{36,35,34,33,27,py}
+skip_missing_interpreters = True
+toxworkdir = /tmp/tox_ipython
 
 [testenv]
+; PyPy requires its Numpy fork instead of "pip install numpy"
+; Other IPython/testing dependencies should be in setup.py, not here
 deps =
-  pyzmq
-  nose
-  tornado<4.0
-  jinja2
-  sphinx
-  pygments
-  jsonpointer
-  jsonschema
-  mistune
+  pypy: https://bitbucket.org/pypy/numpy/get/master.zip
+  py{36,35,34,33,27}: matplotlib
+  .[test]
 
-# To avoid loading IPython module in the current directory, change
-# current directory to ".tox/py*/tmp" before running test.
+; It's just to avoid loading the IPython package in the current directory
 changedir = {envtmpdir}
 
-commands =
-  iptest --all
-
-[testenv:py27]
-deps=
-  mock
-  {[testenv]deps}
+commands = iptest {posargs}

diff --git a/IPython/lib/tests/test_pretty.py b/IPython/lib/tests/test_pretty.py
index 699549563..6f11e99cb 100644
--- a/IPython/lib/tests/test_pretty.py
+++ b/IPython/lib/tests/test_pretty.py
@@ -7,11 +7,13 @@
 from __future__ import print_function
 
 from collections import Counter, defaultdict, deque, OrderedDict
+import types, string, ctypes
 
 import nose.tools as nt
 
 from IPython.lib import pretty
-from IPython.testing.decorators import skip_without, py2_only
+from IPython.testing.decorators import (skip_without, py2_only, py3_only,
+                                        cpython2_only)
 from IPython.utils.py3compat import PY3, unicode_to_str
 
 if PY3:
@@ -186,12 +188,14 @@ class SB(SA):
     pass
 
 def test_super_repr():
+    # "<super: module_name.SA, None>"
     output = pretty.pretty(super(SA))
-    nt.assert_in("SA", output)
+    nt.assert_regexp_matches(output, r"<super: \S+.SA, None>")
 
+    # "<super: module_name.SA, <module_name.SB at 0x...>>"
     sb = SB()
     output = pretty.pretty(super(SA, sb))
-    nt.assert_in("SA", output)
+    nt.assert_regexp_matches(output, r"<super: \S+.SA,\s+<\S+.SB at 0x\S+>>")
 
 
 def test_long_list():
@@ -436,3 +440,97 @@ class MyCounter(Counter):
     ]
     for obj, expected in cases:
         nt.assert_equal(pretty.pretty(obj), expected)
+
+@py3_only
+def test_mappingproxy():
+    MP = types.MappingProxyType
+    underlying_dict = {}
+    mp_recursive = MP(underlying_dict)
+    underlying_dict[2] = mp_recursive
+    underlying_dict[3] = underlying_dict
+
+    cases = [
+        (MP({}), "mappingproxy({})"),
+        (MP({None: MP({})}), "mappingproxy({None: mappingproxy({})})"),
+        (MP({k: k.upper() for k in string.ascii_lowercase}),
+         "mappingproxy({'a': 'A',\n"
+         "              'b': 'B',\n"
+         "              'c': 'C',\n"
+         "              'd': 'D',\n"
+         "              'e': 'E',\n"
+         "              'f': 'F',\n"
+         "              'g': 'G',\n"
+         "              'h': 'H',\n"
+         "              'i': 'I',\n"
+         "              'j': 'J',\n"
+         "              'k': 'K',\n"
+         "              'l': 'L',\n"
+         "              'm': 'M',\n"
+         "              'n': 'N',\n"
+         "              'o': 'O',\n"
+         "              'p': 'P',\n"
+         "              'q': 'Q',\n"
+         "              'r': 'R',\n"
+         "              's': 'S',\n"
+         "              't': 'T',\n"
+         "              'u': 'U',\n"
+         "              'v': 'V',\n"
+         "              'w': 'W',\n"
+         "              'x': 'X',\n"
+         "              'y': 'Y',\n"
+         "              'z': 'Z'})"),
+        (mp_recursive, "mappingproxy({2: {...}, 3: {2: {...}, 3: {...}}})"),
+        (underlying_dict,
+         "{2: mappingproxy({2: {...}, 3: {...}}), 3: {...}}"),
+    ]
+    for obj, expected in cases:
+        nt.assert_equal(pretty.pretty(obj), expected)
+
+@cpython2_only # In PyPy, types.DictProxyType is dict
+def test_dictproxy():
+    # This is the dictproxy constructor itself from the Python API,
+    DP = ctypes.pythonapi.PyDictProxy_New
+    DP.argtypes, DP.restype = (ctypes.py_object,), ctypes.py_object
+
+    underlying_dict = {}
+    mp_recursive = DP(underlying_dict)
+    underlying_dict[0] = mp_recursive
+    underlying_dict[-3] = underlying_dict
+
+    cases = [
+        (DP({}), "dict_proxy({})"),
+        (DP({None: DP({})}), "dict_proxy({None: dict_proxy({})})"),
+        (DP({k: k.lower() for k in string.ascii_uppercase}),
+         "dict_proxy({'A': 'a',\n"
+         "            'B': 'b',\n"
+         "            'C': 'c',\n"
+         "            'D': 'd',\n"
+         "            'E': 'e',\n"
+         "            'F': 'f',\n"
+         "            'G': 'g',\n"
+         "            'H': 'h',\n"
+         "            'I': 'i',\n"
+         "            'J': 'j',\n"
+         "            'K': 'k',\n"
+         "            'L': 'l',\n"
+         "            'M': 'm',\n"
+         "            'N': 'n',\n"
+         "            'O': 'o',\n"
+         "            'P': 'p',\n"
+         "            'Q': 'q',\n"
+         "            'R': 'r',\n"
+         "            'S': 's',\n"
+         "            'T': 't',\n"
+         "            'U': 'u',\n"
+         "            'V': 'v',\n"
+         "            'W': 'w',\n"
+         "            'X': 'x',\n"
+         "            'Y': 'y',\n"
+         "            'Z': 'z'})"),
+        (mp_recursive, "dict_proxy({-3: {-3: {...}, 0: {...}}, 0: {...}})"),
+    ]
+    for obj, expected in cases:
+        nt.assert_is_instance(obj, types.DictProxyType) # Meta-test
+        nt.assert_equal(pretty.pretty(obj), expected)
+    nt.assert_equal(pretty.pretty(underlying_dict),
+                    "{-3: {...}, 0: dict_proxy({-3: {...}, 0: {...}})}")
diff --git a/IPython/testing/decorators.py b/IPython/testing/decorators.py
index a337254ca..087555d46 100644
--- a/IPython/testing/decorators.py
+++ b/IPython/testing/decorators.py
@@ -48,7 +48,7 @@
 from IPython.external.decorators import *
 
 # For onlyif_cmd_exists decorator
-from IPython.utils.py3compat import string_types, which, PY2, PY3
+from IPython.utils.py3compat import string_types, which, PY2, PY3, PYPY
 
 #-----------------------------------------------------------------------------
 # Classes and functions
@@ -336,6 +336,7 @@ def skip_file_no_x11(name):
 known_failure_py3 = knownfailureif(sys.version_info[0] >= 3, 
                                     'This test is known to fail on Python 3.')
 
+cpython2_only = skipif(PY3 or PYPY, "This test only runs on CPython 2.")
 py2_only = skipif(PY3, "This test only runs on Python 2.")
 py3_only = skipif(PY2, "This test only runs on Python 3.")
 

Pretty printing types.MappingProxyType
[Since Python 3.3](https://docs.python.org/3/library/types.html#types.MappingProxyType), `types.MappingProxyType` replaces the old `types.DictProxyType` from Python 2, but now it can be instantiated. However, pretty printing it is showing only its unsorted oneliner `repr(obj)` result.

```python
In [1]: import types, string

In [2]: types.MappingProxyType({k: k for k in string.ascii_letters})
Out[2]: mappingproxy({'W': 'W', 'L': 'L', 'f': 'f', 'o': 'o', 'p': 'p', 'J': 'J', 'k': 'k', 'r': 'r', 'M': 'M', 'b': 'b', 'u': 'u', 'U': 'U', 'S': 'S', 'w': 'w', 's': 's', 'G': 'G', 'l': 'l', 'I': 'I', 'R': 'R', 'H': 'H', 'e': 'e', 'g': 'g', 'K': 'K', 'v': 'v', 't': 't', 'B': 'B', 'x': 'x', 'n': 'n', 'Y': 'Y', 'O': 'O', 'c': 'c', 'F': 'F', 'z': 'z', 'd': 'd', 'a': 'a', 'q': 'q', 'm': 'm', 'Q': 'Q', 'j': 'j', 'h': 'h', 'X': 'X', 'i': 'i', 'P': 'P', 'V': 'V', 'N': 'N', 'E': 'E', 'y': 'y', 'D': 'D', 'Z': 'Z', 'C': 'C', 'A': 'A', 'T': 'T'})
```

Tested in Python 3.5.2, IPython 5.0.0. I'm fixing this one myself due to #9776 
IPython/lib/tests/test_pretty.py::test_indentation IPython/lib/tests/test_pretty.py::test_dispatch IPython/lib/tests/test_pretty.py::test_callability_checking IPython/lib/tests/test_pretty.py::test_pprint_heap_allocated_type IPython/lib/tests/test_pretty.py::test_pprint_nomod IPython/lib/tests/test_pretty.py::test_pprint_break IPython/lib/tests/test_pretty.py::test_pprint_break_repr IPython/lib/tests/test_pretty.py::test_bad_repr IPython/lib/tests/test_pretty.py::test_really_bad_repr IPython/lib/tests/test_pretty.py::test_super_repr IPython/lib/tests/test_pretty.py::test_long_list IPython/lib/tests/test_pretty.py::test_long_set IPython/lib/tests/test_pretty.py::test_long_tuple IPython/lib/tests/test_pretty.py::test_long_dict IPython/lib/tests/test_pretty.py::test_unbound_method IPython/lib/tests/test_pretty.py::test_metaclass_repr IPython/lib/tests/test_pretty.py::test_unicode_repr IPython/lib/tests/test_pretty.py::test_basic_class IPython/lib/tests/test_pretty.py::test_collections_defaultdict IPython/lib/tests/test_pretty.py::test_collections_ordereddict IPython/lib/tests/test_pretty.py::test_collections_deque IPython/lib/tests/test_pretty.py::test_collections_counter IPython/lib/tests/test_pretty.py::test_mappingproxy