diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index 7322bd9fe3327..c48f6d19e3b10 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -647,6 +647,7 @@ Groupby/Resample/Rolling
 - Bug in :func:`DataFrame.groupby` where aggregation by ``first``/``last``/``min``/``max`` was causing timestamps to lose precision (:issue:`19526`)
 - Bug in :func:`DataFrame.transform` where particular aggregation functions were being incorrectly cast to match the dtype(s) of the grouped data (:issue:`19200`)
 - Bug in :func:`DataFrame.groupby` passing the `on=` kwarg, and subsequently using ``.apply()`` (:issue:`17813`)
+- Bug in :func:`DataFrame.resample().aggregate` not raising a `ValueError` when aggregating a non-existent column (:issue:`16766`)
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/base.py b/pandas/core/base.py
index d5b204dba063e..0969717d85e4f 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -392,6 +392,10 @@ def nested_renaming_depr(level=4):
 
                     elif isinstance(obj, ABCSeries):
                         nested_renaming_depr()
+                    elif isinstance(obj, ABCDataFrame) and \
+                            k not in obj.columns:
+                        raise ValueError(
+                            "Column '{col}' does not exist!".format(col=k))
 
                 arg = new_arg
 
diff --git a/pandas/tests/test_resample.py b/pandas/tests/test_resample.py
index 2de890ea459f0..9feba3fd042dd 100644
--- a/pandas/tests/test_resample.py
+++ b/pandas/tests/test_resample.py
@@ -20,7 +20,6 @@
 
 from pandas.core.dtypes.generic import ABCSeries, ABCDataFrame
 from pandas.compat import range, lrange, zip, product, OrderedDict
-from pandas.core.base import SpecificationError
 from pandas.errors import UnsupportedFunctionCall
 from pandas.core.groupby import DataError
 import pandas.core.common as com
@@ -614,7 +613,7 @@ def f():
                     t[['A']].agg({'A': ['sum', 'std'],
                                   'B': ['mean', 'std']})
 
-            pytest.raises(SpecificationError, f)
+            pytest.raises(ValueError, f)
 
     def test_agg_nested_dicts(self):
 
@@ -659,6 +658,21 @@ def f():
                                 'B': {'rb': ['mean', 'std']}})
             assert_frame_equal(result, expected, check_like=True)
 
+    def test_try_aggregate_non_existing_column(self):
+        # GH 16766
+        data = [
+            {'dt': datetime(2017, 6, 1, 0), 'x': 1.0, 'y': 2.0},
+            {'dt': datetime(2017, 6, 1, 1), 'x': 2.0, 'y': 2.0},
+            {'dt': datetime(2017, 6, 1, 2), 'x': 3.0, 'y': 1.5}
+        ]
+        df = DataFrame(data).set_index('dt')
+
+        # Error as we don't have 'z' column
+        with pytest.raises(ValueError):
+            df.resample('30T').agg({'x': ['mean'],
+                                    'y': ['median'],
+                                    'z': ['sum']})
+
     def test_selection_api_validation(self):
         # GH 13500
         index = date_range(datetime(2005, 1, 1),