diff --git a/pandas/core/arrays/set.py b/pandas/core/arrays/set.py
new file mode 100644
index 0000000000000..d4a307270c74a
--- /dev/null
+++ b/pandas/core/arrays/set.py
@@ -0,0 +1,443 @@
+import sys
+import warnings
+import copy
+import numpy as np
+
+import operator
+
+from pandas import Series
+
+# from pandas._libs.lib import infer_dtype
+from pandas.util._decorators import cache_readonly
+from pandas.compat import u, range
+from pandas.compat import set_function_name
+
+from pandas.core.dtypes.common import (
+    is_integer, is_scalar, is_object_dtype, is_list_like)
+from pandas.core.arrays import ExtensionArray, ExtensionOpsMixin
+from pandas.core.dtypes.base import ExtensionDtype
+from pandas.core.dtypes.dtypes import registry
+from pandas.core.dtypes.missing import isna
+
+from pandas.io.formats.printing import (
+    format_object_summary, format_object_attrs, default_pprint)
+
+
+class SetDtype(ExtensionDtype):
+    """
+    An ExtensionDtype to hold sets.
+    """
+    name = 'set'
+    type = object
+    na_value = np.nan
+
+    def __hash__(self):
+        # XXX: this needs to be part of the interface.
+        return hash(str(self))
+
+    def __eq__(self, other):
+        # TODO: test
+        if isinstance(other, type(self)):
+            return True
+        else:
+            return super(SetDtype, self).__eq__(other)
+
+    @property
+    def _is_numeric(self):
+        return False
+
+    def __repr__(self):
+        return self.name
+
+    @classmethod
+    def construct_array_type(cls):
+        """Return the array type associated with this dtype
+
+        Returns
+        -------
+        type
+        """
+        return SetArray
+
+    @classmethod
+    def construct_from_string(cls, string):
+        """
+        Construction from a string, raise a TypeError if not
+        possible
+        """
+        if string == cls.name or string is set:
+            return cls()
+        raise TypeError("Cannot construct a '{}' from "
+                        "'{}'".format(cls, string))
+
+#     @classmethod
+#     def is_dtype(cls, dtype):
+#         dtype = getattr(dtype, 'dtype', dtype)
+#         if (isinstance(dtype, compat.string_types) and
+#                 dtype == 'set'):
+#             return True
+#         elif isinstance(dtype, cls):
+#             return True
+#         return isinstance(dtype, np.dtype) or dtype == 'set'
+
+
+def to_set_array(values):
+    """
+    Infer and return a set array of the values.
+
+    Parameters
+    ----------
+    values : 1D list-like of list-likes
+
+    Returns
+    -------
+    SetArray
+
+    Raises
+    ------
+    TypeError if incompatible types
+    """
+    return SetArray(values, copy=False)
+
+
+def coerce_to_array(values, mask=None, copy=False):
+    """
+    Coerce the input values array to numpy arrays with a mask
+
+    Parameters
+    ----------
+    values : 1D list-like
+    mask : boolean 1D array, optional
+    copy : boolean, default False
+        if True, copy the input
+
+    Returns
+    -------
+    tuple of (values, mask)
+    """
+
+    if isinstance(values, SetArray):
+        values, mask = values._data, values._mask
+
+        if copy:
+            values = values.copy()
+            mask = mask.copy()
+        return values, mask
+
+    values = np.array(values, copy=copy)
+    if not (is_object_dtype(values) or isna(values).all()):
+        raise TypeError("{} cannot be converted to a SetDtype".format(
+            values.dtype))
+
+    if mask is None:
+        mask = isna(values)
+    else:
+        assert len(mask) == len(values)
+
+    if not values.ndim == 1:
+        raise TypeError("values must be a 1D list-like")
+    if not mask.ndim == 1:
+        raise TypeError("mask must be a 1D list-like")
+
+    if mask.any():
+        values = values.copy()
+        values[mask] = np.nan
+
+    return values, mask
+
+
+class SetArray(ExtensionArray, ExtensionOpsMixin):
+    """
+    We represent a SetArray with 2 numpy arrays
+    - data: contains a numpy set array of object dtype
+    - mask: a boolean array holding a mask on the data, False is missing
+    """
+
+    @cache_readonly
+    def dtype(self):
+        return SetDtype()
+
+    def __init__(self, values, mask=None, dtype=None, copy=False):
+        """
+        Parameters
+        ----------
+        values : 1D list-like / SetArray
+        mask : 1D list-like, optional
+        copy : bool, default False
+
+        Returns
+        -------
+        SetArray
+        """
+        self._data, self._mask = coerce_to_array(
+            values, mask=mask, copy=copy)
+
+    @classmethod
+    def _from_sequence(cls, scalars, dtype=None, copy=False):
+        # dtype is ignored
+        return cls(scalars, copy=copy)
+
+    @classmethod
+    def _from_factorized(cls, values, original):
+        return cls(values)
+
+    def __getitem__(self, item):
+        if is_integer(item):
+            if self._mask[item]:
+                return self.dtype.na_value
+            return self._data[item]
+        return type(self)(self._data[item], mask=self._mask[item])
+
+    def _coerce_to_ndarray(self):
+        """
+        coerce to an ndarray of object dtype
+        """
+        data = self._data
+        data[self._mask] = self._na_value
+        return data
+
+    def __array__(self):
+        """
+        the array interface, return values
+        """
+        return self._coerce_to_ndarray()
+
+    def __iter__(self):
+        """Iterate over elements of the array.
+
+        """
+        # This needs to be implemented so that pandas recognizes extension
+        # arrays as list-like. The default implementation makes successive
+        # calls to ``__getitem__``, which may be slower than necessary.
+        for i in range(len(self)):
+            if self._mask[i]:
+                yield self.dtype.na_value
+            else:
+                yield self._data[i]
+
+    def _formatting_values(self):
+        # type: () -> np.ndarray
+        return self._coerce_to_ndarray()
+
+    def take(self, indices, allow_fill=False, fill_value=None):
+        from pandas.core.algorithms import take
+
+        if allow_fill and fill_value is None:
+            fill_value = self.dtype.na_value
+
+        result = take(self._data, indices, fill_value=fill_value,
+                      allow_fill=allow_fill)
+        return self._from_sequence(result)
+
+    def copy(self, deep=False):
+        data, mask = self._data, self._mask
+        if deep:
+            data = copy.deepcopy(data)
+            mask = copy.deepcopy(mask)
+        else:
+            data = data.copy()
+            mask = mask.copy()
+        return type(self)(data, mask, copy=False)
+
+    def __setitem__(self, key, value):
+        _is_scalar = is_scalar(value)
+        if _is_scalar:
+            value = [value]
+        value, mask = coerce_to_array(value)
+
+        if _is_scalar:
+            value = value[0]
+            mask = mask[0]
+
+        self._data[key] = value
+        self._mask[key] = mask
+
+    def __len__(self):
+        return len(self._data)
+
+    def __repr__(self):
+        """
+        Return a string representation for this object.
+
+        Invoked by unicode(df) in py2 only. Yields a Unicode String in both
+        py2/py3.
+        """
+        klass = self.__class__.__name__
+        data = format_object_summary(self, default_pprint, False)
+        attrs = format_object_attrs(self)
+        space = " "
+
+        prepr = (u(",%s") %
+                 space).join(u("%s=%s") % (k, v) for k, v in attrs)
+
+        res = u("%s(%s%s)") % (klass, data, prepr)
+
+        return res
+
+    @property
+    def nbytes(self):
+        return self._data.nbytes + self._mask.nbytes
+
+    def isna(self):
+        return self._mask
+
+    @property
+    def _na_value(self):
+        return np.nan
+
+    @classmethod
+    def _concat_same_type(cls, to_concat):
+        data = np.concatenate([x._data for x in to_concat])
+        mask = np.concatenate([x._mask for x in to_concat])
+        return cls(data, mask=mask)
+
+    def astype(self, dtype, copy=True, errors='raise', fill_value=None):
+        """Cast to a NumPy array or SetArray with 'dtype'.
+
+        Parameters
+        ----------
+        dtype : str or dtype
+            Typecode or data-type to which the array is cast.
+        copy : bool, default True
+            Whether to copy the data, even if not necessary. If False,
+            a copy is made only if the old dtype does not match the
+            new dtype.
+
+        Returns
+        -------
+        array : ndarray or SetArray
+            NumPy ndarray or SetArray with 'dtype' for its dtype.
+
+        Raises
+        ------
+        TypeError
+            if incompatible type with a SetDtype, equivalent of same_kind
+            casting
+        """
+
+        # if we are astyping to an existing IntegerDtype we can fastpath
+        if isinstance(dtype, SetDtype):
+            result = self._data.astype(dtype.type,
+                                       casting='same_kind', copy=False)
+            return type(self)(result, mask=self._mask, copy=False)
+
+        # coerce
+        data = self._coerce_to_ndarray()
+        return data.astype(dtype, copy=False)
+
+    @property
+    def _ndarray_values(self):
+        # type: () -> np.ndarray
+        """Internal pandas method for lossy conversion to a NumPy ndarray.
+
+        This method is not part of the pandas interface.
+
+        The expectation is that this is cheap to compute, and is primarily
+        used for interacting with our indexers.
+        """
+        return self._data
+
+    def fillna(self, value=None, method=None, limit=None):
+        # TODO: method/limit
+        res = self._data.copy()
+        res[self._mask] = [value] * self._mask.sum()
+        return type(self)(res,
+                          mask=np.full_like(res, fill_value=False, dtype=bool),
+                          copy=False)
+
+    def dropna(self):
+        res = self._data[~self._mask]
+        return type(self)(res,
+                          mask=np.full_like(res, fill_value=False, dtype=bool),
+                          copy=False)
+
+    def unique(self):
+        raise NotImplementedError
+
+    def factorize(self):
+        raise NotImplementedError
+
+    def argsort(self):
+        raise NotImplementedError
+
+    def value_counts(self, dropna=True):
+        raise NotImplementedError
+
+    def _values_for_argsort(self):
+        raise NotImplementedError
+
+    @classmethod
+    def _create_comparison_method(cls, op):
+        def cmp_method(self, other):
+
+            op_name = op.__name__
+            mask = None
+            if isinstance(other, SetArray):
+                other, mask = other._data, other._mask
+            elif (isinstance(other, Series)
+                  and isinstance(other.values, SetArray)):
+                other, mask = other.values._data, other.values._mask
+            elif isinstance(other, set) or (is_scalar(other) and isna(other)):
+                other = np.array([other] * len(self))
+            elif is_list_like(other):
+                other = np.asarray(other)
+                if other.ndim > 0 and len(self) != len(other):
+                    raise ValueError('Lengths must match to compare')
+
+            mask = self._mask | mask if mask is not None else self._mask
+            result = np.full_like(self._data, fill_value=np.nan, dtype='O')
+
+            # numpy will show a DeprecationWarning on invalid elementwise
+            # comparisons, this will raise in the future
+            with warnings.catch_warnings(record=True):
+                with np.errstate(all='ignore'):
+                    result[~mask] = op(self._data[~mask], other[~mask])
+
+            result[mask] = True if op_name == 'ne' else False
+            return result.astype('bool')
+
+        name = '__{name}__'.format(name=op.__name__)
+        return set_function_name(cmp_method, name, cls)
+
+    @classmethod
+    def _create_arithmetic_method(cls, op):
+        def arithmetic_method(self, other):
+
+            mask = None
+            if isinstance(other, SetArray):
+                other, mask = other._data, other._mask
+            elif isinstance(other, set) or (is_scalar(other) and isna(other)):
+                other = np.array([other] * len(self))
+            elif is_list_like(other):
+                other = np.asarray(other)
+                # cannot use isnan due to numpy/numpy#9009
+                mask = np.array([x is np.nan for x in other])
+                if other.ndim > 0 and len(self) != len(other):
+                    raise ValueError('Lengths must match to compare')
+
+            mask = self._mask | mask if mask is not None else self._mask
+            result = np.full_like(self._data, fill_value=np.nan, dtype='O')
+
+            with np.errstate(all='ignore'):
+                result[~mask] = op(self._data[~mask], other[~mask])
+
+            return type(self)(result, mask=mask, copy=False)
+
+        name = '__{name}__'.format(name=op.__name__)
+
+        def raiser(self, other):
+            raise NotImplementedError
+        if name != '__sub__':
+            return raiser
+        return set_function_name(arithmetic_method, name, cls)
+
+
+SetArray._add_comparison_ops()
+SetArray._add_arithmetic_ops()
+SetArray.__or__ = SetArray._create_arithmetic_method(operator.__or__)
+SetArray.__xor__ = SetArray._create_arithmetic_method(operator.__xor__)
+SetArray.__and__ = SetArray._create_arithmetic_method(operator.__and__)
+
+module = sys.modules[__name__]
+setattr(module, 'SetDtype', SetDtype)
+registry.register(SetDtype)
diff --git a/pandas/core/ops.py b/pandas/core/ops.py
index dc139a8e14f66..50135d18cc21f 100644
--- a/pandas/core/ops.py
+++ b/pandas/core/ops.py
@@ -1151,7 +1151,9 @@ def dispatch_to_extension_op(op, left, right):
                 new_right = [new_right]
             new_right = list(new_right)
         elif is_extension_array_dtype(right) and type(left) != type(right):
-            new_right = list(new_right)
+            new_right = new_right.astype(left.dtype).values
+        elif is_extension_array_dtype(right):
+            new_right = right.values
         else:
             new_right = right
 
@@ -1482,6 +1484,45 @@ def _bool_method_SERIES(cls, op, special):
     code duplication.
     """
 
+    def dispatch_to_extension_op(op, left, right):
+        """
+        Assume that left or right is a Series backed by an ExtensionArray,
+        apply the operator defined by op.
+        """
+
+        # The op calls will raise TypeError if the op is not defined
+        # on the ExtensionArray
+        # TODO(jreback)
+        # we need to listify to avoid ndarray, or non-same-type extension array
+        # dispatching
+
+        if is_extension_array_dtype(left):
+
+            new_left = left.values
+            if isinstance(right, np.ndarray):
+
+                # handle numpy scalars, this is a PITA
+                # TODO(jreback)
+                new_right = lib.item_from_zerodim(right)
+                if is_scalar(new_right):
+                    new_right = [new_right]
+                new_right = list(new_right)
+            elif is_extension_array_dtype(right) and type(left) != type(right):
+                new_right = new_right.astype(left.dtype).values
+            elif is_extension_array_dtype(right):
+                new_right = right.values
+            else:
+                new_right = right
+
+        else:
+            new_left = left
+            new_right = right.values._data
+
+        res_values = op(new_left, new_right)
+        res_name = get_op_result_name(left, right)
+
+        return _construct_result(left, res_values, left.index, res_name)
+
     def na_op(x, y):
         try:
             result = op(x, y)
@@ -1516,12 +1557,20 @@ def na_op(x, y):
     def wrapper(self, other):
         is_self_int_dtype = is_integer_dtype(self.dtype)
 
-        self, other = _align_method_SERIES(self, other, align_asobject=True)
+        align_asobject = not (is_extension_array_dtype(self) or
+                              is_extension_array_dtype(other))
+        self, other = _align_method_SERIES(self, other,
+                                           align_asobject=align_asobject)
 
         if isinstance(other, ABCDataFrame):
             # Defer to DataFrame implementation; fail early
             return NotImplemented
 
+        elif (is_extension_array_dtype(self)
+              or is_extension_array_dtype(other)):
+            # TODO: should this include `not is_scalar(right)`?
+            return dispatch_to_extension_op(op, self, other)
+
         elif isinstance(other, ABCSeries):
             name = get_op_result_name(self, other)
             is_other_int_dtype = is_integer_dtype(other.dtype)
diff --git a/pandas/tests/extension/base/ops.py b/pandas/tests/extension/base/ops.py
index f7bfdb8ec218a..de88e6dfdbef8 100644
--- a/pandas/tests/extension/base/ops.py
+++ b/pandas/tests/extension/base/ops.py
@@ -69,7 +69,8 @@ def test_arith_series_with_array(self, data, all_arithmetic_operators):
         # ndarray & other series
         op_name = all_arithmetic_operators
         s = pd.Series(data)
-        self.check_opname(s, op_name, [s.iloc[0]] * len(s), exc=TypeError)
+        self.check_opname(s, op_name, pd.Series([s.iloc[0]] * len(s)),
+                          exc=TypeError)
 
     def test_divmod(self, data):
         s = pd.Series(data)
@@ -108,10 +109,10 @@ def _compare_other(self, s, data, op_name, other):
     def test_compare_scalar(self, data, all_compare_operators):
         op_name = all_compare_operators
         s = pd.Series(data)
-        self._compare_other(s, data, op_name, 0)
+        self._compare_other(s, data, op_name, data[0])
 
     def test_compare_array(self, data, all_compare_operators):
         op_name = all_compare_operators
         s = pd.Series(data)
-        other = [0] * len(data)
+        other = pd.Series([data[0]] * len(data))
         self._compare_other(s, data, op_name, other)
diff --git a/pandas/tests/extension/set/__init__.py b/pandas/tests/extension/set/__init__.py
new file mode 100644
index 0000000000000..e69de29bb2d1d
diff --git a/pandas/tests/extension/set/test_set.py b/pandas/tests/extension/set/test_set.py
new file mode 100644
index 0000000000000..428fed4ecccb6
--- /dev/null
+++ b/pandas/tests/extension/set/test_set.py
@@ -0,0 +1,159 @@
+import numpy as np
+import pandas.util.testing as tm
+import pytest
+
+from pandas.tests.extension import base
+
+from pandas.core.arrays.set import SetDtype, SetArray
+
+
+def make_string_sets():
+    s = tm.makeStringSeries()
+    return s.index.map(set).values
+
+
+def make_int_sets():
+    s = tm.makeFloatSeries().astype(str).str.replace(r'\D', '')
+    return s.map(lambda x: set(map(int, x))).values
+
+
+def make_data():
+    return (list(make_string_sets()) +
+            [np.nan] +
+            list(make_int_sets()) +
+            [np.nan, None, set()])
+
+
+@pytest.fixture
+def dtype():
+    return SetDtype()
+
+
+@pytest.fixture
+def data():
+    return SetArray(make_int_sets())
+
+
+@pytest.fixture
+def data_missing():
+    return SetArray([np.nan, {1}])
+
+
+@pytest.fixture
+def data_repeated(data):
+    def gen(count):
+        for _ in range(count):
+            yield data
+    yield gen
+
+
+# @pytest.fixture
+# def data_for_sorting(dtype):
+#     return SetArray(...)
+
+
+# @pytest.fixture
+# def data_missing_for_sorting(dtype):
+#     return SetArray(...)
+
+
+@pytest.fixture
+def na_cmp():
+    # we are np.nan
+    return lambda x, y: np.isnan(x) and np.isnan(y)
+
+
+@pytest.fixture
+def na_value():
+    return np.nan
+
+# @pytest.fixture
+# def data_for_grouping(dtype):
+#     return SetArray(...)
+
+
+class TestDtype(base.BaseDtypeTests):
+
+    def test_array_type_with_arg(self, data, dtype):
+        assert dtype.construct_array_type() is SetArray
+
+
+class TestInterface(base.BaseInterfaceTests):
+
+    def test_len(self, data):
+        assert len(data) == 30
+
+
+class TestConstructors(base.BaseConstructorsTests):
+    pass
+
+
+class TestReshaping(base.BaseReshapingTests):
+    pass
+
+
+class TestGetitem(base.BaseGetitemTests):
+
+    @pytest.mark.skip(reason="Need to think about it.")
+    def test_take_non_na_fill_value(self, data_missing):
+        pass
+
+
+class TestSetitem(base.BaseGetitemTests):
+    pass
+
+
+class TestMissing(base.BaseMissingTests):
+
+    def test_fillna_frame(self, data_missing):
+        pytest.skip('df.fillna does not dispatch to EA')
+
+    def test_fillna_limit_pad(self):
+        pytest.skip('TODO')
+
+    def test_fillna_limit_backfill(self):
+        pytest.skip('TODO')
+
+    def test_fillna_series_method(self):
+        pytest.skip('TODO')
+
+    def test_fillna_series(self):
+        pytest.skip('series.fillna does not dispatch to EA')
+
+
+# # most methods (value_counts, unique, factorize) will not be for SetArray
+# # rest still buggy
+class TestMethods(base.BaseMethodsTests):
+    pass
+
+
+class TestCasting(base.BaseCastingTests):
+    pass
+
+
+class TestArithmeticOps(base.BaseArithmeticOpsTests):
+
+    def check_opname(self, s, op_name, other, exc='ignored'):
+        op = self.get_op_from_name(op_name)
+
+        self._check_op(s, op, other,
+                       None if op_name == '__sub__' else NotImplementedError)
+
+    def test_divmod(self, data):
+        pytest.skip('Not relevant')
+
+    def test_error(self, data, all_arithmetic_operators):
+        pytest.skip('TODO')
+
+
+class TestComparisonOps(base.BaseComparisonOpsTests):
+
+    def _compare_other(self, s, data, op_name, other):
+        op = self.get_op_from_name(op_name)
+        result = op(s, other)
+        expected = s.combine(other, op)
+        self.assert_series_equal(result, expected)
+
+# # GroupBy won't be implemented for SetArray
+# class TestGroupby(base.BaseGroupbyTests):
+#     pass