diff --git a/zarr/core.py b/zarr/core.py
index eb054e4e6b..61ea8752d4 100644
--- a/zarr/core.py
+++ b/zarr/core.py
@@ -268,7 +268,7 @@ def ndim(self):
 
     @property
     def _size(self):
-        return reduce(operator.mul, self._shape)
+        return reduce(operator.mul, self._shape, 1)
 
     @property
     def size(self):
@@ -313,8 +313,11 @@ def nbytes_stored(self):
 
     @property
     def _cdata_shape(self):
-        return tuple(int(np.ceil(s / c))
-                     for s, c in zip(self._shape, self._chunks))
+        if self._shape == ():
+            return (1,)
+        else:
+            return tuple(int(np.ceil(s / c))
+                         for s, c in zip(self._shape, self._chunks))
 
     @property
     def cdata_shape(self):
@@ -325,7 +328,7 @@ def cdata_shape(self):
 
     @property
     def _nchunks(self):
-        return reduce(operator.mul, self._cdata_shape)
+        return reduce(operator.mul, self._cdata_shape, 1)
 
     @property
     def nchunks(self):
@@ -360,13 +363,16 @@ def __eq__(self, other):
         )
 
     def __array__(self, *args):
-        a = self[:]
+        a = self[...]
         if args:
             a = a.astype(args[0])
         return a
 
     def __len__(self):
-        return self.shape[0]
+        if self.shape:
+            return self.shape[0]
+        else:
+            raise TypeError('len() of unsized object')
 
     def __getitem__(self, item):
         """Retrieve data for some portion of the array. Most NumPy-style
@@ -443,6 +449,41 @@ def __getitem__(self, item):
         if not self._cache_metadata:
             self._load_metadata()
 
+        # handle zero-dimensional arrays
+        if self._shape == ():
+            return self._getitem_zd(item)
+        else:
+            return self._getitem_nd(item)
+
+    def _getitem_zd(self, item):
+        # special case __getitem__ for zero-dimensional array
+
+        # check item is valid
+        if item not in ((), Ellipsis):
+            raise IndexError('too many indices for array')
+
+        try:
+            # obtain encoded data for chunk
+            ckey = self._chunk_key((0,))
+            cdata = self.chunk_store[ckey]
+
+        except KeyError:
+            # chunk not initialized
+            out = np.empty((), dtype=self._dtype)
+            if self._fill_value is not None:
+                out.fill(self._fill_value)
+
+        else:
+            out = self._decode_chunk(cdata)
+
+        # handle selection of the scalar value via empty tuple
+        out = out[item]
+
+        return out
+
+    def _getitem_nd(self, item):
+        # implementation of __getitem__ for array with at least one dimension
+
         # normalize selection
         selection = normalize_array_selection(item, self._shape)
 
@@ -559,6 +600,36 @@ def __setitem__(self, item, value):
         if not self._cache_metadata:
             self._load_metadata_nosync()
 
+        # handle zero-dimensional arrays
+        if self._shape == ():
+            return self._setitem_zd(item, value)
+        else:
+            return self._setitem_nd(item, value)
+
+    def _setitem_zd(self, item, value):
+        # special case __setitem__ for zero-dimensional array
+
+        # check item is valid
+        if item not in ((), Ellipsis):
+            raise IndexError('too many indices for array')
+
+        # setup data to store
+        arr = np.asarray(value, dtype=self._dtype)
+
+        # check value
+        if arr.shape != ():
+            raise ValueError('bad value; expected scalar, found %r' % value)
+
+        # obtain key for chunk storage
+        ckey = self._chunk_key((0,))
+
+        # encode and store
+        cdata = self._encode_chunk(arr)
+        self.chunk_store[ckey] = cdata
+
+    def _setitem_nd(self, item, value):
+        # implementation of __setitem__ for array with at least one dimension
+
         # normalize selection
         selection = normalize_array_selection(item, self._shape)
 
@@ -570,7 +641,7 @@ def __setitem__(self, item, value):
         if np.isscalar(value):
             pass
         elif expected_shape != value.shape:
-            raise ValueError('value has wrong shape, expecting %s, found %s'
+            raise ValueError('value has wrong shape; expected %s, found %s'
                              % (str(expected_shape),
                                 str(value.shape)))
 
@@ -646,6 +717,7 @@ def _chunk_getitem(self, cidx, item, dest):
                 # optimization: we want the whole chunk, and the destination is
                 # contiguous, so we can decompress directly from the chunk
                 # into the destination array
+
                 if self._compressor:
                     self._compressor.decode(cdata, dest)
                 else:
diff --git a/zarr/creation.py b/zarr/creation.py
index c40977eb43..ec32de64bc 100644
--- a/zarr/creation.py
+++ b/zarr/creation.py
@@ -320,7 +320,7 @@ def array(data, **kwargs):
     z = create(**kwargs)
 
     # fill with data
-    z[:] = data
+    z[...] = data
 
     return z
 
diff --git a/zarr/storage.py b/zarr/storage.py
index 782361bae1..aa6e949139 100644
--- a/zarr/storage.py
+++ b/zarr/storage.py
@@ -279,19 +279,23 @@ def _init_array_metadata(store, shape, chunks=None, dtype=None, compressor='defa
     chunks = normalize_chunks(chunks, shape, dtype.itemsize)
     order = normalize_order(order)
 
-    # obtain compressor config
-    if compressor == 'none':
+    # compressor prep
+    if shape == ():
+        # no point in compressing a 0-dimensional array, only a single value
+        compressor = None
+    elif compressor == 'none':
         # compatibility
         compressor = None
     elif compressor == 'default':
         compressor = default_compressor
+
+    # obtain compressor config
+    compressor_config = None
     if compressor:
         try:
             compressor_config = compressor.get_config()
         except AttributeError:
             err_bad_compressor(compressor)
-    else:
-        compressor_config = None
 
     # obtain filters config
     if filters:
diff --git a/zarr/tests/test_core.py b/zarr/tests/test_core.py
index 90885cea91..1ef8bd9f33 100644
--- a/zarr/tests/test_core.py
+++ b/zarr/tests/test_core.py
@@ -158,6 +158,8 @@ def test_array_1d_fill_value(self):
             assert_array_equal(f[310:], z[310:])
 
     def test_array_1d_set_scalar(self):
+        # test setting the contents of an array with a scalar value
+
         # setup
         a = np.zeros(100)
         z = self.create_array(shape=a.shape, chunks=10, dtype=a.dtype)
@@ -587,6 +589,52 @@ def test_0len_dim_2d(self):
         with assert_raises(IndexError):
             z[:, 0] = 42
 
+    def test_array_0d(self):
+        # test behaviour for array with 0 dimensions
+
+        # setup
+        a = np.zeros(())
+        z = self.create_array(shape=(), dtype=a.dtype, fill_value=0)
+
+        # check properties
+        eq(a.ndim, z.ndim)
+        eq(a.shape, z.shape)
+        eq(a.size, z.size)
+        eq(a.dtype, z.dtype)
+        eq(a.nbytes, z.nbytes)
+        with assert_raises(TypeError):
+            len(z)
+        eq((), z.chunks)
+        eq(1, z.nchunks)
+        eq((1,), z.cdata_shape)
+        # compressor always None - no point in compressing a single value
+        assert_is_none(z.compressor)
+
+        # check __getitem__
+        b = z[...]
+        assert_is_instance(b, np.ndarray)
+        eq(a.shape, b.shape)
+        eq(a.dtype, b.dtype)
+        assert_array_equal(a, np.array(z))
+        assert_array_equal(a, z[...])
+        eq(a[()], z[()])
+        with assert_raises(IndexError):
+            z[0]
+        with assert_raises(IndexError):
+            z[:]
+
+        # check __setitem__
+        z[...] = 42
+        eq(42, z[()])
+        z[()] = 43
+        eq(43, z[()])
+        with assert_raises(IndexError):
+            z[0] = 42
+        with assert_raises(IndexError):
+            z[:] = 42
+        with assert_raises(ValueError):
+            z[...] = np.array([1, 2, 3])
+
 
 class TestArrayWithPath(TestArray):
 
diff --git a/zarr/tests/test_hierarchy.py b/zarr/tests/test_hierarchy.py
index 2f34d0e3dc..4ab1073dae 100644
--- a/zarr/tests/test_hierarchy.py
+++ b/zarr/tests/test_hierarchy.py
@@ -641,6 +641,10 @@ def test_setitem(self):
             data = np.arange(200)
             g['foo'] = data
             assert_array_equal(data, g['foo'])
+            # 0d array
+            g['foo'] = 42
+            eq((), g['foo'].shape)
+            eq(42, g['foo'][()])
         except NotImplementedError:
             pass