diff --git a/ci/requirements-py37.yml b/ci/requirements-py37.yml
index fe5afd589c8..723ad24d24d 100644
--- a/ci/requirements-py37.yml
+++ b/ci/requirements-py37.yml
@@ -30,3 +30,4 @@ dependencies:
   - pydap
   - pip:
     - mypy==0.650
+    - numbagg
diff --git a/doc/api.rst b/doc/api.rst
index 33c8d9d3ceb..811e3241438 100644
--- a/doc/api.rst
+++ b/doc/api.rst
@@ -148,6 +148,7 @@ Computation
    Dataset.groupby
    Dataset.groupby_bins
    Dataset.rolling
+   Dataset.rolling_exp
    Dataset.coarsen
    Dataset.resample
    Dataset.diff
@@ -315,6 +316,7 @@ Computation
    DataArray.groupby
    DataArray.groupby_bins
    DataArray.rolling
+   DataArray.rolling_exp
    DataArray.coarsen
    DataArray.dt
    DataArray.resample
@@ -535,6 +537,7 @@ Rolling objects
    core.rolling.DatasetRolling
    core.rolling.DatasetRolling.construct
    core.rolling.DatasetRolling.reduce
+   core.rolling_exp.RollingExp
 
 Resample objects
 ================
diff --git a/doc/computation.rst b/doc/computation.rst
index 3100925a7d3..b06d7959504 100644
--- a/doc/computation.rst
+++ b/doc/computation.rst
@@ -190,6 +190,22 @@ We can also manually iterate through ``Rolling`` objects:
    for label, arr_window in r:
       # arr_window is a view of x
 
+.. _comput.rolling_exp:
+
+While ``rolling`` provides a simple moving average, ``DataArray`` also supports
+an exponential moving average with :py:meth:`~xarray.DataArray.rolling_exp`.
+This is similiar to pandas' ``ewm`` method. numbagg_ is required.
+
+.. _numbagg: https://github.com/shoyer/numbagg
+
+.. code:: python
+
+    arr.rolling_exp(y=3).mean()
+
+The ``rolling_exp`` method takes a ``window_type`` kwarg, which can be ``'alpha'``,
+``'com'`` (for ``center-of-mass``), ``'span'``, and ``'halflife'``. The default is
+``span``.
+
 Finally, the rolling object has a ``construct`` method which returns a
 view of the original ``DataArray`` with the windowed dimension in
 the last position.
diff --git a/doc/installing.rst b/doc/installing.rst
index f624da18611..b9d1b4d0ba4 100644
--- a/doc/installing.rst
+++ b/doc/installing.rst
@@ -45,6 +45,8 @@ For accelerating xarray
 - `bottleneck <https://github.com/kwgoodman/bottleneck>`__: speeds up
   NaN-skipping and rolling window aggregations by a large factor
   (1.1 or later)
+- `numbagg <https://github.com/shoyer/numbagg>`_: for exponential rolling
+  window operations
 
 For parallel computing
 ~~~~~~~~~~~~~~~~~~~~~~
diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index ca50856a25e..c5b9a01a09e 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -30,6 +30,11 @@ Enhancements
 - Add ``fill_value`` argument for reindex, align, and merge operations
   to enable custom fill values. (:issue:`2876`)
   By `Zach Griffith <https://github.com/zdgriffith>`_.
+- :py:meth:`~xarray.DataArray.rolling_exp` and
+  :py:meth:`~xarray.Dataset.rolling_exp` added, similar to pandas' 
+  ``pd.DataFrame.ewm`` method. Calling ``.mean`` on the resulting object 
+  will return an exponentially weighted moving average.
+  By `Maximilian Roos <https://github.com/max-sixty>`_.
 - Character arrays' character dimension name decoding and encoding handled by
   ``var.encoding['char_dim_name']`` (:issue:`2895`)
   By `James McCreight <https://github.com/jmccreight>`_.
@@ -188,6 +193,7 @@ Other enhancements
 - Upsampling an array via interpolation with resample is now dask-compatible,
   as long as the array is not chunked along the resampling dimension.
   By `Spencer Clark <https://github.com/spencerkclark>`_.
+  
 - :py:func:`xarray.testing.assert_equal` and
   :py:func:`xarray.testing.assert_identical` now provide a more detailed
   report showing what exactly differs between the two objects (dimensions /
@@ -737,7 +743,7 @@ Enhancements
   arguments in ``data_vars`` to indexes set explicitly in ``coords``,
   where previously an error would be raised.
   (:issue:`674`)
-  By `Maximilian Roos <https://github.com/maxim-lian>`_.
+  By `Maximilian Roos <https://github.com/max-sixty>`_.
 
 - :py:meth:`~DataArray.sel`, :py:meth:`~DataArray.isel` & :py:meth:`~DataArray.reindex`,
   (and their :py:class:`Dataset` counterparts) now support supplying a ``dict``
@@ -745,12 +751,12 @@ Enhancements
   of supplying `kwargs`. This allows for more robust behavior
   of dimension names which conflict with other keyword names, or are
   not strings.
-  By `Maximilian Roos <https://github.com/maxim-lian>`_.
+  By `Maximilian Roos <https://github.com/max-sixty>`_.
 
 - :py:meth:`~DataArray.rename` now supports supplying ``**kwargs``, as an
   alternative to the existing approach of supplying a ``dict`` as the
   first argument.
-  By `Maximilian Roos <https://github.com/maxim-lian>`_.
+  By `Maximilian Roos <https://github.com/max-sixty>`_.
 
 - :py:meth:`~DataArray.cumsum` and :py:meth:`~DataArray.cumprod` now support
   aggregation over multiple dimensions at the same time. This is the default
@@ -915,7 +921,7 @@ Enhancements
   which test each value in the array for whether it is contained in the
   supplied list, returning a bool array. See :ref:`selecting values with isin`
   for full details. Similar to the ``np.isin`` function.
-  By `Maximilian Roos <https://github.com/maxim-lian>`_.
+  By `Maximilian Roos <https://github.com/max-sixty>`_.
 - Some speed improvement to construct :py:class:`~xarray.DataArrayRolling`
   object (:issue:`1993`)
   By `Keisuke Fujii <https://github.com/fujiisoup>`_.
@@ -2110,7 +2116,7 @@ Enhancements
 ~~~~~~~~~~~~
 
 - New documentation on :ref:`panel transition`. By
-  `Maximilian Roos <https://github.com/maximilianr>`_.
+  `Maximilian Roos <https://github.com/max-sixty>`_.
 - New ``Dataset`` and ``DataArray`` methods :py:meth:`~xarray.Dataset.to_dict`
   and :py:meth:`~xarray.Dataset.from_dict` to allow easy conversion between
   dictionaries and xarray objects (:issue:`432`). See
@@ -2131,9 +2137,9 @@ Bug fixes
   (:issue:`953`). By `Stephan Hoyer <https://github.com/shoyer>`_.
 - ``Dataset.__dir__()`` (i.e. the method python calls to get autocomplete
   options) failed if one of the dataset's keys was not a string (:issue:`852`).
-  By `Maximilian Roos <https://github.com/maximilianr>`_.
+  By `Maximilian Roos <https://github.com/max-sixty>`_.
 - ``Dataset`` constructor can now take arbitrary objects as values
-  (:issue:`647`). By `Maximilian Roos <https://github.com/maximilianr>`_.
+  (:issue:`647`). By `Maximilian Roos <https://github.com/max-sixty>`_.
 - Clarified ``copy`` argument for :py:meth:`~xarray.DataArray.reindex` and
   :py:func:`~xarray.align`, which now consistently always return new xarray
   objects (:issue:`927`).
diff --git a/setup.cfg b/setup.cfg
index cdfe2ec3e36..bfa49118d84 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -9,8 +9,11 @@ filterwarnings =
     ignore:Using a non-tuple sequence for multidimensional indexing is deprecated:FutureWarning
 env =
     UVCDAT_ANONYMOUS_LOG=no
+markers =
+    flaky: flaky tests
+    network: tests requiring a network connection
+    slow: slow tests
 
-# This should be kept in sync with .pep8speaks.yml
 [flake8]
 max-line-length=79
 ignore=
@@ -23,10 +26,6 @@ ignore=
     F401
 exclude=
     doc
-markers =
-    flaky: flaky tests
-    network: tests requiring a network connection
-    slow: slow tests
 
 [isort]
 default_section=THIRDPARTY
@@ -62,6 +61,8 @@ ignore_missing_imports = True
 ignore_missing_imports = True
 [mypy-nc_time_axis.*]
 ignore_missing_imports = True
+[mypy-numbagg.*]
+ignore_missing_imports = True
 [mypy-numpy.*]
 ignore_missing_imports = True
 [mypy-netCDF4.*]
diff --git a/xarray/core/common.py b/xarray/core/common.py
index 4e5133fd8c6..0195be62500 100644
--- a/xarray/core/common.py
+++ b/xarray/core/common.py
@@ -12,6 +12,7 @@
 from .arithmetic import SupportsArithmetic
 from .options import _get_keep_attrs
 from .pycompat import dask_array_type
+from .rolling_exp import RollingExp
 from .utils import Frozen, ReprObject, SortedKeysDict, either_dict_or_kwargs
 
 # Used as a sentinel value to indicate a all dimensions
@@ -86,6 +87,7 @@ def wrapped_func(self, dim=None, **kwargs):  # type: ignore
 class AbstractArray(ImplementsArrayReduce):
     """Shared base class for DataArray and Variable.
     """
+
     def __bool__(self: Any) -> bool:
         return bool(self.values)
 
@@ -249,6 +251,8 @@ def get_squeeze_dims(xarray_obj,
 class DataWithCoords(SupportsArithmetic, AttrAccessMixin):
     """Shared base class for Dataset and DataArray."""
 
+    _rolling_exp_cls = RollingExp
+
     def squeeze(self, dim: Union[Hashable, Iterable[Hashable], None] = None,
                 drop: bool = False,
                 axis: Union[int, Iterable[int], None] = None):
@@ -553,7 +557,7 @@ def groupby_bins(self, group, bins, right: bool = True, labels=None,
 
     def rolling(self, dim: Optional[Mapping[Hashable, int]] = None,
                 min_periods: Optional[int] = None, center: bool = False,
-                **dim_kwargs: int):
+                **window_kwargs: int):
         """
         Rolling window object.
 
@@ -568,9 +572,9 @@ def rolling(self, dim: Optional[Mapping[Hashable, int]] = None,
             setting min_periods equal to the size of the window.
         center : boolean, default False
             Set the labels at the center of the window.
-        **dim_kwargs : optional
+        **window_kwargs : optional
             The keyword arguments form of ``dim``.
-            One of dim or dim_kwargs must be provided.
+            One of dim or window_kwargs must be provided.
 
         Returns
         -------
@@ -609,15 +613,54 @@ def rolling(self, dim: Optional[Mapping[Hashable, int]] = None,
         core.rolling.DataArrayRolling
         core.rolling.DatasetRolling
         """  # noqa
-        dim = either_dict_or_kwargs(dim, dim_kwargs, 'rolling')
+        dim = either_dict_or_kwargs(dim, window_kwargs, 'rolling')
         return self._rolling_cls(self, dim, min_periods=min_periods,
                                  center=center)
 
+    def rolling_exp(
+        self,
+        window: Optional[Mapping[Hashable, int]] = None,
+        window_type: str = 'span',
+        **window_kwargs
+    ):
+        """
+        Exponentially-weighted moving window.
+        Similar to EWM in pandas
+
+        Requires the optional Numbagg dependency.
+
+        Parameters
+        ----------
+        window : A single mapping from a dimension name to window value,
+                 optional
+            dim : str
+                Name of the dimension to create the rolling exponential window
+                along (e.g., `time`).
+            window : int
+                Size of the moving window. The type of this is specified in
+                `window_type`
+        window_type : str, one of ['span', 'com', 'halflife', 'alpha'],
+                      default 'span'
+            The format of the previously supplied window. Each is a simple
+            numerical transformation of the others. Described in detail:
+            https://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.ewm.html
+        **window_kwargs : optional
+            The keyword arguments form of ``window``.
+            One of window or window_kwargs must be provided.
+
+        See Also
+        --------
+        core.rolling_exp.RollingExp
+        """
+        window = either_dict_or_kwargs(window, window_kwargs, 'rolling_exp')
+
+        return self._rolling_exp_cls(self, window, window_type)
+
     def coarsen(self, dim: Optional[Mapping[Hashable, int]] = None,
                 boundary: str = 'exact',
                 side: Union[str, Mapping[Hashable, str]] = 'left',
                 coord_func: str = 'mean',
-                **dim_kwargs: int):
+                **window_kwargs: int):
         """
         Coarsen object.
 
@@ -671,7 +714,7 @@ def coarsen(self, dim: Optional[Mapping[Hashable, int]] = None,
         core.rolling.DataArrayCoarsen
         core.rolling.DatasetCoarsen
         """
-        dim = either_dict_or_kwargs(dim, dim_kwargs, 'coarsen')
+        dim = either_dict_or_kwargs(dim, window_kwargs, 'coarsen')
         return self._coarsen_cls(
             self, dim, boundary=boundary, side=side,
             coord_func=coord_func)
diff --git a/xarray/core/rolling_exp.py b/xarray/core/rolling_exp.py
new file mode 100644
index 00000000000..ff6baef5c3a
--- /dev/null
+++ b/xarray/core/rolling_exp.py
@@ -0,0 +1,106 @@
+import numpy as np
+
+from .pycompat import dask_array_type
+
+
+def _get_alpha(com=None, span=None, halflife=None, alpha=None):
+    # pandas defines in terms of com (converting to alpha in the algo)
+    # so use its function to get a com and then convert to alpha
+
+    com = _get_center_of_mass(com, span, halflife, alpha)
+    return 1 / (1 + com)
+
+
+def move_exp_nanmean(array, *, axis, alpha):
+    if isinstance(array, dask_array_type):
+        raise TypeError("rolling_exp is not currently support for dask arrays")
+    import numbagg
+    if axis == ():
+        return array.astype(np.float64)
+    else:
+        return numbagg.move_exp_nanmean(
+            array, axis=axis, alpha=alpha)
+
+
+def _get_center_of_mass(comass, span, halflife, alpha):
+    """
+    Vendored from pandas.core.window._get_center_of_mass
+
+    See licenses/PANDAS_LICENSE for the function's license
+    """
+    from pandas.core import common as com
+    valid_count = com.count_not_none(comass, span, halflife, alpha)
+    if valid_count > 1:
+        raise ValueError("comass, span, halflife, and alpha "
+                         "are mutually exclusive")
+
+    # Convert to center of mass; domain checks ensure 0 < alpha <= 1
+    if comass is not None:
+        if comass < 0:
+            raise ValueError("comass must satisfy: comass >= 0")
+    elif span is not None:
+        if span < 1:
+            raise ValueError("span must satisfy: span >= 1")
+        comass = (span - 1) / 2.
+    elif halflife is not None:
+        if halflife <= 0:
+            raise ValueError("halflife must satisfy: halflife > 0")
+        decay = 1 - np.exp(np.log(0.5) / halflife)
+        comass = 1 / decay - 1
+    elif alpha is not None:
+        if alpha <= 0 or alpha > 1:
+            raise ValueError("alpha must satisfy: 0 < alpha <= 1")
+        comass = (1.0 - alpha) / alpha
+    else:
+        raise ValueError("Must pass one of comass, span, halflife, or alpha")
+
+    return float(comass)
+
+
+class RollingExp:
+    """
+    Exponentially-weighted moving window object.
+    Similar to EWM in pandas
+
+    Parameters
+    ----------
+    obj : Dataset or DataArray
+        Object to window.
+    windows : A single mapping from a single dimension name to window value
+        dim : str
+            Name of the dimension to create the rolling exponential window
+            along (e.g., `time`).
+        window : int
+            Size of the moving window. The type of this is specified in
+            `window_type`
+    window_type : str, one of ['span', 'com', 'halflife', 'alpha'], default 'span'
+        The format of the previously supplied window. Each is a simple
+        numerical transformation of the others. Described in detail:
+        https://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.ewm.html
+
+    Returns
+    -------
+    RollingExp : type of input argument
+    """  # noqa
+
+    def __init__(self, obj, windows, window_type='span'):
+        self.obj = obj
+        dim, window = next(iter(windows.items()))
+        self.dim = dim
+        self.alpha = _get_alpha(**{window_type: window})
+
+    def mean(self):
+        """
+        Exponentially weighted moving average
+
+        Examples
+        --------
+        >>> da = xr.DataArray([1,1,2,2,2], dims='x')
+        >>> da.rolling_exp(x=2, window_type='span').mean()
+        <xarray.DataArray (x: 5)>
+        array([1.      , 1.      , 1.692308, 1.9     , 1.966942])
+        Dimensions without coordinates: x
+        """
+
+        return self.obj.reduce(
+            move_exp_nanmean, dim=self.dim, alpha=self.alpha)
diff --git a/xarray/tests/__init__.py b/xarray/tests/__init__.py
index dc8b26e4524..81bb1a1e18d 100644
--- a/xarray/tests/__init__.py
+++ b/xarray/tests/__init__.py
@@ -74,6 +74,7 @@ def LooseVersion(vstring):
 has_np113, requires_np113 = _importorskip('numpy', minversion='1.13.0')
 has_iris, requires_iris = _importorskip('iris')
 has_cfgrib, requires_cfgrib = _importorskip('cfgrib')
+has_numbagg, requires_numbagg = _importorskip('numbagg')
 
 # some special cases
 has_h5netcdf07, requires_h5netcdf07 = _importorskip('h5netcdf',
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index a8825055479..beb77f343fa 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -20,7 +20,7 @@
     LooseVersion, ReturnItem, assert_allclose, assert_array_equal,
     assert_equal, assert_identical, raises_regex, requires_bottleneck,
     requires_cftime, requires_dask, requires_iris, requires_np113,
-    requires_scipy, source_ndarray)
+    requires_numbagg, requires_scipy, source_ndarray)
 
 
 class TestDataArray:
@@ -3919,14 +3919,14 @@ def test_to_and_from_iris(self):
             assert coord.var_name == original_coord.name
             assert_array_equal(
                 coord.points, CFDatetimeCoder().encode(original_coord).values)
-            assert (actual.coord_dims(coord) ==
-                    original.get_axis_num(
+            assert (actual.coord_dims(coord)
+                    == original.get_axis_num(
                         original.coords[coord.var_name].dims))
 
-        assert (actual.coord('distance2').attributes['foo'] ==
-                original.coords['distance2'].attrs['foo'])
-        assert (actual.coord('distance').units ==
-                cf_units.Unit(original.coords['distance'].units))
+        assert (actual.coord('distance2').attributes['foo']
+                == original.coords['distance2'].attrs['foo'])
+        assert (actual.coord('distance').units
+                == cf_units.Unit(original.coords['distance'].units))
         assert actual.attributes['baz'] == original.attrs['baz']
         assert actual.standard_name == original.attrs['standard_name']
 
@@ -3984,14 +3984,14 @@ def test_to_and_from_iris_dask(self):
             assert coord.var_name == original_coord.name
             assert_array_equal(
                 coord.points, CFDatetimeCoder().encode(original_coord).values)
-            assert (actual.coord_dims(coord) ==
-                    original.get_axis_num(
+            assert (actual.coord_dims(coord)
+                    == original.get_axis_num(
                         original.coords[coord.var_name].dims))
 
         assert (actual.coord('distance2').attributes['foo'] == original.coords[
             'distance2'].attrs['foo'])
-        assert (actual.coord('distance').units ==
-                cf_units.Unit(original.coords['distance'].units))
+        assert (actual.coord('distance').units
+                == cf_units.Unit(original.coords['distance'].units))
         assert actual.attributes['baz'] == original.attrs['baz']
         assert actual.standard_name == original.attrs['standard_name']
 
@@ -4087,3 +4087,30 @@ def test_fallback_to_iris_AuxCoord(self, coord_values):
         expected = Cube(data, aux_coords_and_dims=[
             (AuxCoord(coord_values, var_name='space'), 0)])
         assert result == expected
+
+
+@requires_numbagg
+@pytest.mark.parametrize('dim', ['time', 'x'])
+@pytest.mark.parametrize('window_type, window', [
+    ['span', 5],
+    ['alpha', 0.5],
+    ['com', 0.5],
+    ['halflife', 5],
+])
+def test_rolling_exp(da, dim, window_type, window):
+    da = da.isel(a=0)
+    da = da.where(da > 0.2)
+
+    result = da.rolling_exp(window_type=window_type, **{dim: window}).mean()
+    assert isinstance(result, DataArray)
+
+    pandas_array = da.to_pandas()
+    assert pandas_array.index.name == 'time'
+    if dim == 'x':
+        pandas_array = pandas_array.T
+    expected = (
+        xr.DataArray(pandas_array.ewm(**{window_type: window}).mean())
+        .transpose(*da.dims)
+    )
+
+    assert_allclose(expected.variable, result.variable)
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 8cd129e35de..afbdd51b464 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -23,7 +23,7 @@
     InaccessibleArray, UnexpectedDataAccess, assert_allclose,
     assert_array_equal, assert_equal, assert_identical, has_cftime, has_dask,
     raises_regex, requires_bottleneck, requires_cftime, requires_dask,
-    requires_scipy, source_ndarray)
+    requires_numbagg, requires_scipy, source_ndarray)
 
 try:
     import dask.array as da
@@ -4809,6 +4809,13 @@ def test_rolling_wrapped_bottleneck(ds, name, center, min_periods, key):
     assert_equal(actual, ds['time'])
 
 
+@requires_numbagg
+def test_rolling_exp(ds):
+
+    result = ds.rolling_exp(time=10, window_type='span').mean()
+    assert isinstance(result, Dataset)
+
+
 @pytest.mark.parametrize('center', (True, False))
 @pytest.mark.parametrize('min_periods', (None, 1, 2, 3))
 @pytest.mark.parametrize('window', (1, 2, 3, 4))
diff --git a/xarray/util/print_versions.py b/xarray/util/print_versions.py
index 50389df85cb..c34faa7487b 100755
--- a/xarray/util/print_versions.py
+++ b/xarray/util/print_versions.py
@@ -108,6 +108,7 @@ def show_versions(as_json=False):
         ("matplotlib", lambda mod: mod.__version__),
         ("cartopy", lambda mod: mod.__version__),
         ("seaborn", lambda mod: mod.__version__),
+        ("numbagg", lambda mod: mod.__version__),
         # xarray setup/test
         ("setuptools", lambda mod: mod.__version__),
         ("pip", lambda mod: mod.__version__),