diff --git a/.travis.yml b/.travis.yml
index 0a71e7dc1d7..d3dce9141dc 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -20,9 +20,11 @@ env:
     - TOXENV=py27-pexpect
     - TOXENV=py27-xdist
     - TOXENV=py27-trial
+    - TOXENV=py27-numpy
     - TOXENV=py35-pexpect
     - TOXENV=py35-xdist
     - TOXENV=py35-trial
+    - TOXENV=py35-numpy
     - TOXENV=py27-nobyte
     - TOXENV=doctesting
     - TOXENV=freeze
diff --git a/_pytest/compat.py b/_pytest/compat.py
index 8c200af5fe5..0554efeb704 100644
--- a/_pytest/compat.py
+++ b/_pytest/compat.py
@@ -125,6 +125,7 @@ def isclass(object):
 if _PY3:
     import codecs
     imap = map
+    izip = zip
     STRING_TYPES = bytes, str
     UNICODE_TYPES = str,
 
@@ -160,7 +161,7 @@ def _escape_strings(val):
     STRING_TYPES = bytes, str, unicode
     UNICODE_TYPES = unicode,
 
-    from itertools import imap  # NOQA
+    from itertools import imap, izip  # NOQA
 
     def _escape_strings(val):
         """In py2 bytes and str are the same type, so return if it's a bytes
diff --git a/_pytest/python_api.py b/_pytest/python_api.py
index 1b27ba32758..cb7d5e4590e 100644
--- a/_pytest/python_api.py
+++ b/_pytest/python_api.py
@@ -3,13 +3,279 @@
 
 import py
 
-from _pytest.compat import isclass
+from _pytest.compat import isclass, izip
 from _pytest.runner import fail
 import _pytest._code
+
 # builtin pytest.approx helper
 
+class ApproxBase(object):
+    """
+    Provide shared utilities for making approximate comparisons between numbers
+    or sequences of numbers.
+    """
+
+    def __init__(self, expected, rel=None, abs=None, nan_ok=False):
+        self.expected = expected
+        self.abs = abs
+        self.rel = rel
+        self.nan_ok = nan_ok
+
+    def __repr__(self):
+        raise NotImplementedError
+
+    def __eq__(self, actual):
+        return all(
+                a == self._approx_scalar(x)
+                for a, x in self._yield_comparisons(actual))
+
+    __hash__ = None
+
+    def __ne__(self, actual):
+        return not (actual == self)
+
+    def _approx_scalar(self, x):
+        return ApproxScalar(x, rel=self.rel, abs=self.abs, nan_ok=self.nan_ok)
+
+    def _yield_comparisons(self, actual):
+        """
+        Yield all the pairs of numbers to be compared.  This is used to
+        implement the `__eq__` method.
+        """
+        raise NotImplementedError
+
+
+class ApproxNumpyBase(ApproxBase):
+    """
+    Perform approximate comparisons for numpy arrays.
+
+    This class should not be used directly.  Instead, the `inherit_ndarray()`
+    class method should be used to make a subclass that also inherits from
+    `np.ndarray`.  This indirection is necessary because the object doing the
+    approximate comparison must inherit from `np.ndarray`, or it will only work
+    on the left side of the `==` operator.  But importing numpy is relatively
+    expensive, so we also want to avoid that unless we actually have a numpy
+    array to compare.
+
+    The reason why the approx object needs to inherit from `np.ndarray` has to
+    do with how python decides whether to call `a.__eq__()` or `b.__eq__()`
+    when it parses `a == b`.  If `a` and `b` are not related by inheritance,
+    `a` gets priority.  So as long as `a.__eq__` is defined, it will be called.
+    Because most implementations of `a.__eq__` end up calling `b.__eq__`, this
+    detail usually doesn't matter.  However, `np.ndarray.__eq__` treats the
+    approx object as a scalar and builds a new array by comparing it to each
+    item in the original array.  `b.__eq__` is called to compare against each
+    individual element in the array, but it has no way (that I can see) to
+    prevent the return value from being an boolean array, and boolean arrays
+    can't be used with assert because "the truth value of an array with more
+    than one element is ambiguous."
+
+    The trick is that the priority rules change if `a` and `b` are related
+    by inheritance.  Specifically, `b.__eq__` gets priority if `b` is a
+    subclass of `a`.  So by inheriting from `np.ndarray`, we can guarantee that
+    `ApproxNumpy.__eq__` gets called no matter which side of the `==` operator
+    it appears on.
+    """
+
+    subclass = None
+
+    @classmethod
+    def inherit_ndarray(cls):
+        import numpy as np
+        assert not isinstance(cls, np.ndarray)
+
+        if cls.subclass is None:
+            cls.subclass = type('ApproxNumpy', (cls, np.ndarray), {})
+
+        return cls.subclass
+
+    def __new__(cls, expected, rel=None, abs=None, nan_ok=False):
+        """
+        Numpy uses __new__ (rather than __init__) to initialize objects.
+
+        The `expected` argument must be a numpy array.  This should be
+        ensured by the approx() delegator function.
+        """
+        obj = super(ApproxNumpyBase, cls).__new__(cls, ())
+        obj.__init__(expected, rel, abs, nan_ok)
+        return obj
+
+    def __repr__(self):
+        # It might be nice to rewrite this function to account for the
+        # shape of the array...
+        return "approx({0!r})".format(list(
+            self._approx_scalar(x) for x in self.expected))
+
+    def __eq__(self, actual):
+        import numpy as np
+
+        try:
+            actual = np.asarray(actual)
+        except:
+            raise ValueError("cannot cast '{0}' to numpy.ndarray".format(actual))
+
+        if actual.shape != self.expected.shape:
+            return False
+
+        return ApproxBase.__eq__(self, actual)
+
+    def _yield_comparisons(self, actual):
+        import numpy as np
+
+        # We can be sure that `actual` is a numpy array, because it's
+        # casted in `__eq__` before being passed to `ApproxBase.__eq__`,
+        # which is the only method that calls this one.
+        for i in np.ndindex(self.expected.shape):
+            yield actual[i], self.expected[i]
+
+
+class ApproxMapping(ApproxBase):
+    """
+    Perform approximate comparisons for mappings where the values are numbers
+    (the keys can be anything).
+    """
+
+    def __repr__(self):
+        return "approx({0!r})".format(dict(
+            (k, self._approx_scalar(v))
+            for k,v in self.expected.items()))
+
+    def __eq__(self, actual):
+        if set(actual.keys()) != set(self.expected.keys()):
+            return False
+
+        return ApproxBase.__eq__(self, actual)
+
+    def _yield_comparisons(self, actual):
+        for k in self.expected.keys():
+            yield actual[k], self.expected[k]
+
+
+class ApproxSequence(ApproxBase):
+    """
+    Perform approximate comparisons for sequences of numbers.
+    """
+
+    def __repr__(self):
+        seq_type = type(self.expected)
+        if seq_type not in (tuple, list, set):
+            seq_type = list
+        return "approx({0!r})".format(seq_type(
+            self._approx_scalar(x) for x in self.expected))
+
+    def __eq__(self, actual):
+        if len(actual) != len(self.expected):
+            return False
+        return ApproxBase.__eq__(self, actual)
+
+    def _yield_comparisons(self, actual):
+        return izip(actual, self.expected)
+
+
+class ApproxScalar(ApproxBase):
+    """
+    Perform approximate comparisons for single numbers only.
+    """
+
+    def __repr__(self):
+        """
+        Return a string communicating both the expected value and the tolerance
+        for the comparison being made, e.g. '1.0 +- 1e-6'.  Use the unicode
+        plus/minus symbol if this is python3 (it's too hard to get right for
+        python2).
+        """
+        if isinstance(self.expected, complex):
+            return str(self.expected)
+
+        # Infinities aren't compared using tolerances, so don't show a
+        # tolerance.
+        if math.isinf(self.expected):
+            return str(self.expected)
+
+        # If a sensible tolerance can't be calculated, self.tolerance will
+        # raise a ValueError.  In this case, display '???'.
+        try:
+            vetted_tolerance = '{:.1e}'.format(self.tolerance)
+        except ValueError:
+            vetted_tolerance = '???'
+
+        if sys.version_info[0] == 2:
+            return '{0} +- {1}'.format(self.expected, vetted_tolerance)
+        else:
+            return u'{0} \u00b1 {1}'.format(self.expected, vetted_tolerance)
+
+    def __eq__(self, actual):
+        """
+        Return true if the given value is equal to the expected value within
+        the pre-specified tolerance.
+        """
+
+        # Short-circuit exact equality.
+        if actual == self.expected:
+            return True
+
+        # Allow the user to control whether NaNs are considered equal to each
+        # other or not.  The abs() calls are for compatibility with complex
+        # numbers.
+        if math.isnan(abs(self.expected)):
+            return self.nan_ok and math.isnan(abs(actual))
+
+        # Infinity shouldn't be approximately equal to anything but itself, but
+        # if there's a relative tolerance, it will be infinite and infinity
+        # will seem approximately equal to everything.  The equal-to-itself
+        # case would have been short circuited above, so here we can just
+        # return false if the expected value is infinite.  The abs() call is
+        # for compatibility with complex numbers.
+        if math.isinf(abs(self.expected)):
+            return False
+
+        # Return true if the two numbers are within the tolerance.
+        return abs(self.expected - actual) <= self.tolerance
+
+    __hash__ = None
+
+    @property
+    def tolerance(self):
+        """
+        Return the tolerance for the comparison.  This could be either an
+        absolute tolerance or a relative tolerance, depending on what the user
+        specified or which would be larger.
+        """
+        set_default = lambda x, default: x if x is not None else default
+
+        # Figure out what the absolute tolerance should be.  ``self.abs`` is
+        # either None or a value specified by the user.
+        absolute_tolerance = set_default(self.abs, 1e-12)
+
+        if absolute_tolerance < 0:
+            raise ValueError("absolute tolerance can't be negative: {}".format(absolute_tolerance))
+        if math.isnan(absolute_tolerance):
+            raise ValueError("absolute tolerance can't be NaN.")
+
+        # If the user specified an absolute tolerance but not a relative one,
+        # just return the absolute tolerance.
+        if self.rel is None:
+            if self.abs is not None:
+                return absolute_tolerance
+
+        # Figure out what the relative tolerance should be.  ``self.rel`` is
+        # either None or a value specified by the user.  This is done after
+        # we've made sure the user didn't ask for an absolute tolerance only,
+        # because we don't want to raise errors about the relative tolerance if
+        # we aren't even going to use it.
+        relative_tolerance = set_default(self.rel, 1e-6) * abs(self.expected)
+
+        if relative_tolerance < 0:
+            raise ValueError("relative tolerance can't be negative: {}".format(absolute_tolerance))
+        if math.isnan(relative_tolerance):
+            raise ValueError("relative tolerance can't be NaN.")
+
+        # Return the larger of the relative and absolute tolerances.
+        return max(relative_tolerance, absolute_tolerance)
+
+
 
-class approx(object):
+def approx(expected, rel=None, abs=None, nan_ok=False):
     """
     Assert that two numbers (or two sets of numbers) are equal to each other
     within some tolerance.
@@ -45,21 +311,36 @@ class approx(object):
         >>> 0.1 + 0.2 == approx(0.3)
         True
 
-    The same syntax also works on sequences of numbers::
+    The same syntax also works for sequences of numbers::
 
         >>> (0.1 + 0.2, 0.2 + 0.4) == approx((0.3, 0.6))
         True
 
+    Dictionary *values*::
+
+        >>> {'a': 0.1 + 0.2, 'b': 0.2 + 0.4} == approx({'a': 0.3, 'b': 0.6})
+        True
+
+    And ``numpy`` arrays::
+
+        >>> import numpy as np                                                          # doctest: +SKIP
+        >>> np.array([0.1, 0.2]) + np.array([0.2, 0.4]) == approx(np.array([0.3, 0.6])) # doctest: +SKIP
+        True
+
     By default, ``approx`` considers numbers within a relative tolerance of
     ``1e-6`` (i.e. one part in a million) of its expected value to be equal.
     This treatment would lead to surprising results if the expected value was
     ``0.0``, because nothing but ``0.0`` itself is relatively close to ``0.0``.
     To handle this case less surprisingly, ``approx`` also considers numbers
     within an absolute tolerance of ``1e-12`` of its expected value to be
-    equal.  Infinite numbers are another special case.  They are only
-    considered equal to themselves, regardless of the relative tolerance.  Both
-    the relative and absolute tolerances can be changed by passing arguments to
-    the ``approx`` constructor::
+    equal.  Infinity and NaN are special cases.  Infinity is only considered
+    equal to itself, regardless of the relative tolerance.  NaN is not
+    considered equal to anything by default, but you can make it be equal to
+    itself by setting the ``nan_ok`` argument to True.  (This is meant to
+    facilitate comparing arrays that use NaN to mean "no data".)
+
+    Both the relative and absolute tolerances can be changed by passing
+    arguments to the ``approx`` constructor::
 
         >>> 1.0001 == approx(1)
         False
@@ -123,138 +404,54 @@ class approx(object):
       relative tolerance, only the absolute tolerance is considered.
     """
 
-    def __init__(self, expected, rel=None, abs=None):
-        self.expected = expected
-        self.abs = abs
-        self.rel = rel
-
-    def __repr__(self):
-        return ', '.join(repr(x) for x in self.expected)
-
-    def __eq__(self, actual):
-        from collections import Iterable
-        if not isinstance(actual, Iterable):
-            actual = [actual]
-        if len(actual) != len(self.expected):
-            return False
-        return all(a == x for a, x in zip(actual, self.expected))
-
-    __hash__ = None
-
-    def __ne__(self, actual):
-        return not (actual == self)
-
-    @property
-    def expected(self):
-        # Regardless of whether the user-specified expected value is a number
-        # or a sequence of numbers, return a list of ApproxNotIterable objects
-        # that can be compared against.
-        from collections import Iterable
-        approx_non_iter = lambda x: ApproxNonIterable(x, self.rel, self.abs)
-        if isinstance(self._expected, Iterable):
-            return [approx_non_iter(x) for x in self._expected]
-        else:
-            return [approx_non_iter(self._expected)]
+    from collections import Mapping, Sequence
+    from _pytest.compat import STRING_TYPES as String
+
+    # Delegate the comparison to a class that knows how to deal with the type
+    # of the expected value (e.g. int, float, list, dict, numpy.array, etc).
+    #
+    # This architecture is really driven by the need to support numpy arrays.
+    # The only way to override `==` for arrays without requiring that approx be
+    # the left operand is to inherit the approx object from `numpy.ndarray`.
+    # But that can't be a general solution, because it requires (1) numpy to be
+    # installed and (2) the expected value to be a numpy array.  So the general
+    # solution is to delegate each type of expected value to a different class.
+    #
+    # This has the advantage that it made it easy to support mapping types
+    # (i.e. dict).  The old code accepted mapping types, but would only compare
+    # their keys, which is probably not what most people would expect.
+
+    if _is_numpy_array(expected):
+        # Create the delegate class on the fly.  This allow us to inherit from
+        # ``np.ndarray`` while still not importing numpy unless we need to.
+        cls = ApproxNumpyBase.inherit_ndarray()
+    elif isinstance(expected, Mapping):
+        cls = ApproxMapping
+    elif isinstance(expected, Sequence) and not isinstance(expected, String):
+        cls = ApproxSequence
+    else:
+        cls = ApproxScalar
 
-    @expected.setter
-    def expected(self, expected):
-        self._expected = expected
+    return cls(expected, rel, abs, nan_ok)
 
 
-class ApproxNonIterable(object):
+def _is_numpy_array(obj):
     """
-    Perform approximate comparisons for single numbers only.
-
-    In other words, the ``expected`` attribute for objects of this class must
-    be some sort of number.  This is in contrast to the ``approx`` class, where
-    the ``expected`` attribute can either be a number of a sequence of numbers.
-    This class is responsible for making comparisons, while ``approx`` is
-    responsible for abstracting the difference between numbers and sequences of
-    numbers.  Although this class can stand on its own, it's only meant to be
-    used within ``approx``.
+    Return true if the given object is a numpy array.  Make a special effort to
+    avoid importing numpy unless it's really necessary.
     """
+    import inspect
 
-    def __init__(self, expected, rel=None, abs=None):
-        self.expected = expected
-        self.abs = abs
-        self.rel = rel
-
-    def __repr__(self):
-        if isinstance(self.expected, complex):
-            return str(self.expected)
-
-        # Infinities aren't compared using tolerances, so don't show a
-        # tolerance.
-        if math.isinf(self.expected):
-            return str(self.expected)
-
-        # If a sensible tolerance can't be calculated, self.tolerance will
-        # raise a ValueError.  In this case, display '???'.
-        try:
-            vetted_tolerance = '{:.1e}'.format(self.tolerance)
-        except ValueError:
-            vetted_tolerance = '???'
-
-        if sys.version_info[0] == 2:
-            return '{0} +- {1}'.format(self.expected, vetted_tolerance)
-        else:
-            return u'{0} \u00b1 {1}'.format(self.expected, vetted_tolerance)
-
-    def __eq__(self, actual):
-        # Short-circuit exact equality.
-        if actual == self.expected:
-            return True
-
-        # Infinity shouldn't be approximately equal to anything but itself, but
-        # if there's a relative tolerance, it will be infinite and infinity
-        # will seem approximately equal to everything.  The equal-to-itself
-        # case would have been short circuited above, so here we can just
-        # return false if the expected value is infinite.  The abs() call is
-        # for compatibility with complex numbers.
-        if math.isinf(abs(self.expected)):
-            return False
-
-        # Return true if the two numbers are within the tolerance.
-        return abs(self.expected - actual) <= self.tolerance
-
-    __hash__ = None
+    for cls in inspect.getmro(type(obj)):
+        if cls.__module__ == 'numpy':
+            try:
+                import numpy as np
+                return isinstance(obj, np.ndarray)
+            except ImportError:
+                pass
 
-    def __ne__(self, actual):
-        return not (actual == self)
+    return False
 
-    @property
-    def tolerance(self):
-        set_default = lambda x, default: x if x is not None else default
-
-        # Figure out what the absolute tolerance should be.  ``self.abs`` is
-        # either None or a value specified by the user.
-        absolute_tolerance = set_default(self.abs, 1e-12)
-
-        if absolute_tolerance < 0:
-            raise ValueError("absolute tolerance can't be negative: {}".format(absolute_tolerance))
-        if math.isnan(absolute_tolerance):
-            raise ValueError("absolute tolerance can't be NaN.")
-
-        # If the user specified an absolute tolerance but not a relative one,
-        # just return the absolute tolerance.
-        if self.rel is None:
-            if self.abs is not None:
-                return absolute_tolerance
-
-        # Figure out what the relative tolerance should be.  ``self.rel`` is
-        # either None or a value specified by the user.  This is done after
-        # we've made sure the user didn't ask for an absolute tolerance only,
-        # because we don't want to raise errors about the relative tolerance if
-        # we aren't even going to use it.
-        relative_tolerance = set_default(self.rel, 1e-6) * abs(self.expected)
-
-        if relative_tolerance < 0:
-            raise ValueError("relative tolerance can't be negative: {}".format(absolute_tolerance))
-        if math.isnan(relative_tolerance):
-            raise ValueError("relative tolerance can't be NaN.")
-
-        # Return the larger of the relative and absolute tolerances.
-        return max(relative_tolerance, absolute_tolerance)
 
 # builtin pytest.raises helper
 
@@ -282,7 +479,6 @@ def raises(expected_exception, *args, **kwargs):
           ...
         Failed: Expecting ZeroDivisionError
 
-
     .. note::
 
        When using ``pytest.raises`` as a context manager, it's worthwhile to
@@ -315,7 +511,6 @@ def raises(expected_exception, *args, **kwargs):
         >>> with raises(ValueError, match=r'must be \d+$'):
         ...     raise ValueError("value must be 42")
 
-
     Or you can specify a callable by passing a to-be-called lambda::
 
         >>> raises(ZeroDivisionError, lambda: 1/0)
@@ -398,7 +593,6 @@ def raises(expected_exception, *args, **kwargs):
 
 raises.Exception = fail.Exception
 
-
 class RaisesContext(object):
     def __init__(self, expected_exception, message, match_expr):
         self.expected_exception = expected_exception
diff --git a/appveyor.yml b/appveyor.yml
index cc72b4b7053..abf033b4cca 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -20,9 +20,11 @@ environment:
   - TOXENV: "py27-pexpect"
   - TOXENV: "py27-xdist"
   - TOXENV: "py27-trial"
+  - TOXENV: "py27-numpy"
   - TOXENV: "py35-pexpect"
   - TOXENV: "py35-xdist"
   - TOXENV: "py35-trial"
+  - TOXENV: "py35-numpy"
   - TOXENV: "py27-nobyte"
   - TOXENV: "doctesting"
   - TOXENV: "freeze"
diff --git a/changelog/1994.feature b/changelog/1994.feature
new file mode 100644
index 00000000000..f3c596e63b1
--- /dev/null
+++ b/changelog/1994.feature
@@ -0,0 +1 @@
+Add support for numpy arrays (and dicts) to approx.
diff --git a/doc/en/builtin.rst b/doc/en/builtin.rst
index 26dbd44cb3e..af0dd9a744d 100644
--- a/doc/en/builtin.rst
+++ b/doc/en/builtin.rst
@@ -38,7 +38,7 @@ Examples at :ref:`assertraises`.
 Comparing floating point numbers
 --------------------------------
 
-.. autoclass:: approx
+.. autofunction:: approx
 
 Raising a specific test outcome
 --------------------------------------
diff --git a/testing/python/approx.py b/testing/python/approx.py
index d7063e2150f..a21f644f51c 100644
--- a/testing/python/approx.py
+++ b/testing/python/approx.py
@@ -9,7 +9,6 @@
 from fractions import Fraction
 inf, nan = float('inf'), float('nan')
 
-
 class MyDocTestRunner(doctest.DocTestRunner):
 
     def __init__(self):
@@ -29,12 +28,19 @@ def test_repr_string(self):
         if sys.version_info[:2] == (2, 6):
             tol1, tol2, infr = '???', '???', '???'
         assert repr(approx(1.0)) == '1.0 {pm} {tol1}'.format(pm=plus_minus, tol1=tol1)
-        assert repr(approx([1.0, 2.0])) == '1.0 {pm} {tol1}, 2.0 {pm} {tol2}'.format(pm=plus_minus, tol1=tol1, tol2=tol2)
+        assert repr(approx([1.0, 2.0])) == 'approx([1.0 {pm} {tol1}, 2.0 {pm} {tol2}])'.format(pm=plus_minus, tol1=tol1, tol2=tol2)
+        assert repr(approx((1.0, 2.0))) == 'approx((1.0 {pm} {tol1}, 2.0 {pm} {tol2}))'.format(pm=plus_minus, tol1=tol1, tol2=tol2)
         assert repr(approx(inf)) == 'inf'
         assert repr(approx(1.0, rel=nan)) == '1.0 {pm} ???'.format(pm=plus_minus)
         assert repr(approx(1.0, rel=inf)) == '1.0 {pm} {infr}'.format(pm=plus_minus, infr=infr)
         assert repr(approx(1.0j, rel=inf)) == '1j'
 
+        # Dictionaries aren't ordered, so we need to check both orders.
+        assert repr(approx({'a': 1.0, 'b': 2.0})) in (
+                "approx({{'a': 1.0 {pm} {tol1}, 'b': 2.0 {pm} {tol2}}})".format(pm=plus_minus, tol1=tol1, tol2=tol2),
+                "approx({{'b': 2.0 {pm} {tol2}, 'a': 1.0 {pm} {tol1}}})".format(pm=plus_minus, tol1=tol1, tol2=tol2),
+        )
+
     def test_operator_overloading(self):
         assert 1 == approx(1, rel=1e-6, abs=1e-12)
         assert not (1 != approx(1, rel=1e-6, abs=1e-12))
@@ -212,45 +218,18 @@ def test_expecting_inf(self):
 
     def test_expecting_nan(self):
         examples = [
-                (nan, nan),
-                (-nan, -nan),
-                (nan, -nan),
-                (0.0, nan),
-                (inf, nan),
-        ]
-        for a, x in examples:
-            # If there is a relative tolerance and the expected value is NaN,
-            # the actual tolerance is a NaN, which should be an error.
-            with pytest.raises(ValueError):
-                a != approx(x, rel=inf)
-
-            # You can make comparisons against NaN by not specifying a relative
-            # tolerance, so only an absolute tolerance is calculated.
-            assert a != approx(x, abs=inf)
-
-    def test_expecting_sequence(self):
-        within_1e8 = [
-                (1e8 + 1e0, 1e8),
-                (1e0 + 1e-8, 1e0),
-                (1e-8 + 1e-16, 1e-8),
+                (eq, nan, nan),
+                (eq, -nan, -nan),
+                (eq, nan, -nan),
+                (ne, 0.0, nan),
+                (ne, inf, nan),
         ]
-        actual, expected = zip(*within_1e8)
-        assert actual == approx(expected, rel=5e-8, abs=0.0)
-
-    def test_expecting_sequence_wrong_len(self):
-        assert [1, 2] != approx([1])
-        assert [1, 2] != approx([1,2,3])
+        for op, a, x in examples:
+            # Nothing is equal to NaN by default.
+            assert a != approx(x)
 
-    def test_complex(self):
-        within_1e6 = [
-                ( 1.000001 + 1.0j, 1.0 + 1.0j),
-                (1.0 + 1.000001j, 1.0 + 1.0j),
-                (-1.000001 + 1.0j, -1.0 + 1.0j),
-                (1.0 - 1.000001j, 1.0 - 1.0j),
-        ]
-        for a, x in within_1e6:
-            assert a == approx(x, rel=5e-6, abs=0)
-            assert a != approx(x, rel=5e-7, abs=0)
+            # If ``nan_ok=True``, then NaN is equal to NaN.
+            assert op(a, approx(x, nan_ok=True))
 
     def test_int(self):
         within_1e6 = [
@@ -260,6 +239,8 @@ def test_int(self):
         for a, x in within_1e6:
             assert a == approx(x, rel=5e-6, abs=0)
             assert a != approx(x, rel=5e-7, abs=0)
+            assert approx(x, rel=5e-6, abs=0) == a
+            assert approx(x, rel=5e-7, abs=0) != a
 
     def test_decimal(self):
         within_1e6 = [
@@ -269,6 +250,8 @@ def test_decimal(self):
         for a, x in within_1e6:
             assert a == approx(x, rel=Decimal('5e-6'), abs=0)
             assert a != approx(x, rel=Decimal('5e-7'), abs=0)
+            assert approx(x, rel=Decimal('5e-6'), abs=0) == a
+            assert approx(x, rel=Decimal('5e-7'), abs=0) != a
 
     def test_fraction(self):
         within_1e6 = [
@@ -278,6 +261,93 @@ def test_fraction(self):
         for a, x in within_1e6:
             assert a == approx(x, rel=5e-6, abs=0)
             assert a != approx(x, rel=5e-7, abs=0)
+            assert approx(x, rel=5e-6, abs=0) == a
+            assert approx(x, rel=5e-7, abs=0) != a
+
+    def test_complex(self):
+        within_1e6 = [
+                ( 1.000001 + 1.0j, 1.0 + 1.0j),
+                (1.0 + 1.000001j, 1.0 + 1.0j),
+                (-1.000001 + 1.0j, -1.0 + 1.0j),
+                (1.0 - 1.000001j, 1.0 - 1.0j),
+        ]
+        for a, x in within_1e6:
+            assert a == approx(x, rel=5e-6, abs=0)
+            assert a != approx(x, rel=5e-7, abs=0)
+            assert approx(x, rel=5e-6, abs=0) == a
+            assert approx(x, rel=5e-7, abs=0) != a
+
+    def test_list(self):
+        actual = [1 + 1e-7, 2 + 1e-8]
+        expected = [1, 2]
+
+        # Return false if any element is outside the tolerance.
+        assert actual == approx(expected, rel=5e-7, abs=0)
+        assert actual != approx(expected, rel=5e-8, abs=0)
+        assert approx(expected, rel=5e-7, abs=0) == actual
+        assert approx(expected, rel=5e-8, abs=0) != actual
+
+    def test_list_wrong_len(self):
+        assert [1, 2] != approx([1])
+        assert [1, 2] != approx([1,2,3])
+
+    def test_tuple(self):
+        actual = (1 + 1e-7, 2 + 1e-8)
+        expected = (1, 2)
+
+        # Return false if any element is outside the tolerance.
+        assert actual == approx(expected, rel=5e-7, abs=0)
+        assert actual != approx(expected, rel=5e-8, abs=0)
+        assert approx(expected, rel=5e-7, abs=0) == actual
+        assert approx(expected, rel=5e-8, abs=0) != actual
+
+    def test_tuple_wrong_len(self):
+        assert (1, 2) != approx((1,))
+        assert (1, 2) != approx((1,2,3))
+
+    def test_dict(self):
+        actual = {'a': 1 + 1e-7, 'b': 2 + 1e-8}
+        # Dictionaries became ordered in python3.6, so switch up the order here
+        # to make sure it doesn't matter.
+        expected = {'b': 2, 'a': 1}
+
+        # Return false if any element is outside the tolerance.
+        assert actual == approx(expected, rel=5e-7, abs=0)
+        assert actual != approx(expected, rel=5e-8, abs=0)
+        assert approx(expected, rel=5e-7, abs=0) == actual
+        assert approx(expected, rel=5e-8, abs=0) != actual
+
+    def test_dict_wrong_len(self):
+        assert {'a': 1, 'b': 2} != approx({'a': 1})
+        assert {'a': 1, 'b': 2} != approx({'a': 1, 'c': 2})
+        assert {'a': 1, 'b': 2} != approx({'a': 1, 'b': 2, 'c': 3})
+
+    def test_numpy_array(self):
+        np = pytest.importorskip('numpy')
+
+        actual = np.array([1 + 1e-7, 2 + 1e-8])
+        expected = np.array([1, 2])
+
+        # Return false if any element is outside the tolerance.
+        assert actual == approx(expected, rel=5e-7, abs=0)
+        assert actual != approx(expected, rel=5e-8, abs=0)
+        assert approx(expected, rel=5e-7, abs=0) == expected
+        assert approx(expected, rel=5e-8, abs=0) != actual
+
+        # Should be able to compare lists with numpy arrays.
+        assert list(actual) == approx(expected, rel=5e-7, abs=0)
+        assert list(actual) != approx(expected, rel=5e-8, abs=0)
+        assert actual == approx(list(expected), rel=5e-7, abs=0)
+        assert actual != approx(list(expected), rel=5e-8, abs=0)
+
+    def test_numpy_array_wrong_shape(self):
+        np = pytest.importorskip('numpy')
+
+        a12 = np.array([[1, 2]])
+        a21 = np.array([[1],[2]])
+
+        assert a12 != approx(a21)
+        assert a21 != approx(a12)
 
     def test_doctests(self):
         parser = doctest.DocTestParser()
diff --git a/tox.ini b/tox.ini
index b73deca7d32..9b5cdc64a86 100644
--- a/tox.ini
+++ b/tox.ini
@@ -12,7 +12,7 @@ envlist=
      py36
      py37
      pypy
-     {py27,py35}-{pexpect,xdist,trial}
+     {py27,py35}-{pexpect,xdist,trial,numpy}
      py27-nobyte
      doctesting
      freeze
@@ -110,6 +110,16 @@ deps={[testenv:py27-trial]deps}
 commands=
   pytest -ra {posargs:testing/test_unittest.py}
 
+[testenv:py27-numpy]
+deps=numpy
+commands=
+  pytest -rfsxX {posargs:testing/python/approx.py}
+
+[testenv:py35-numpy]
+deps=numpy
+commands=
+  pytest -rfsxX {posargs:testing/python/approx.py}
+
 [testenv:docs]
 skipsdist=True
 usedevelop=True