diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index e97e2d735d9..1d5e584dd2e 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -89,6 +89,8 @@ Bug fixes
 - Line plots with the ``x`` or ``y`` argument set to a 1D non-dimensional coord
   now plot the correct data for 2D DataArrays
   (:issue:`3334`). By `Tom Nicholas <http://github.com/TomNicholas>`_.
+- Make :py:func:`~xarray.concat` more robust when merging variables present in some datasets but
+  not others (:issue:`508`). By `Deepak Cherian <http://github.com/dcherian>`_.
 - The default behaviour of reducing across all dimensions for
   :py:class:`~xarray.core.groupby.DataArrayGroupBy` objects has now been properly removed
   as was done for :py:class:`~xarray.core.groupby.DatasetGroupBy` in 0.13.0 (:issue:`3337`).
diff --git a/xarray/core/concat.py b/xarray/core/concat.py
index ecae2566c02..e98e8a72125 100644
--- a/xarray/core/concat.py
+++ b/xarray/core/concat.py
@@ -312,15 +312,9 @@ def _dataset_concat(
         to_merge = {var: [] for var in variables_to_merge}
 
         for ds in datasets:
-            absent_merge_vars = variables_to_merge - set(ds.variables)
-            if absent_merge_vars:
-                raise ValueError(
-                    "variables %r are present in some datasets but not others. "
-                    % absent_merge_vars
-                )
-
             for var in variables_to_merge:
-                to_merge[var].append(ds.variables[var])
+                if var in ds:
+                    to_merge[var].append(ds.variables[var])
 
         for var in variables_to_merge:
             result_vars[var] = unique_variable(
diff --git a/xarray/tests/test_combine.py b/xarray/tests/test_combine.py
index 6bd1127651c..cd26e7fb60b 100644
--- a/xarray/tests/test_combine.py
+++ b/xarray/tests/test_combine.py
@@ -782,12 +782,11 @@ def test_auto_combine_previously_failed(self):
         actual = auto_combine(datasets, concat_dim="t")
         assert_identical(expected, actual)
 
-    def test_auto_combine_still_fails(self):
-        # concat can't handle new variables (yet):
-        # https://github.com/pydata/xarray/issues/508
+    def test_auto_combine_with_new_variables(self):
         datasets = [Dataset({"x": 0}, {"y": 0}), Dataset({"x": 1}, {"y": 1, "z": 1})]
-        with pytest.raises(ValueError):
-            auto_combine(datasets, "y")
+        actual = auto_combine(datasets, "y")
+        expected = Dataset({"x": ("y", [0, 1])}, {"y": [0, 1], "z": 1})
+        assert_identical(expected, actual)
 
     def test_auto_combine_no_concat(self):
         objs = [Dataset({"x": 0}), Dataset({"y": 1})]
diff --git a/xarray/tests/test_concat.py b/xarray/tests/test_concat.py
index c7af0fc9b35..0661ebb7a38 100644
--- a/xarray/tests/test_concat.py
+++ b/xarray/tests/test_concat.py
@@ -68,6 +68,22 @@ def test_concat_simple(self, data, dim, coords):
         datasets = [g for _, g in data.groupby(dim, squeeze=False)]
         assert_identical(data, concat(datasets, dim, coords=coords))
 
+    def test_concat_merge_variables_present_in_some_datasets(self, data):
+        # coordinates present in some datasets but not others
+        ds1 = Dataset(data_vars={"a": ("y", [0.1])}, coords={"x": 0.1})
+        ds2 = Dataset(data_vars={"a": ("y", [0.2])}, coords={"z": 0.2})
+        actual = concat([ds1, ds2], dim="y", coords="minimal")
+        expected = Dataset({"a": ("y", [0.1, 0.2])}, coords={"x": 0.1, "z": 0.2})
+        assert_identical(expected, actual)
+
+        # data variables present in some datasets but not others
+        split_data = [data.isel(dim1=slice(3)), data.isel(dim1=slice(3, None))]
+        data0, data1 = deepcopy(split_data)
+        data1["foo"] = ("bar", np.random.randn(10))
+        actual = concat([data0, data1], "dim1")
+        expected = data.copy().assign(foo=data1.foo)
+        assert_identical(expected, actual)
+
     def test_concat_2(self, data):
         dim = "dim2"
         datasets = [g for _, g in data.groupby(dim, squeeze=True)]
@@ -190,11 +206,6 @@ def test_concat_errors(self):
             concat([data0, data1], "dim1", compat="identical")
         assert_identical(data, concat([data0, data1], "dim1", compat="equals"))
 
-        with raises_regex(ValueError, "present in some datasets"):
-            data0, data1 = deepcopy(split_data)
-            data1["foo"] = ("bar", np.random.randn(10))
-            concat([data0, data1], "dim1")
-
         with raises_regex(ValueError, "compat.* invalid"):
             concat(split_data, "dim1", compat="foobar")