diff --git a/cpp/include/cudf/utilities/traits.hpp b/cpp/include/cudf/utilities/traits.hpp
index f4e7e3e2a6d..40a833112e1 100644
--- a/cpp/include/cudf/utilities/traits.hpp
+++ b/cpp/include/cudf/utilities/traits.hpp
@@ -142,6 +142,31 @@ constexpr inline bool is_equality_comparable()
   return detail::is_equality_comparable_impl<L, R>::value;
 }
 
+namespace detail {
+/**
+ * @brief Helper functor to check if a specified type `T` supports equality comparisons.
+ */
+struct unary_equality_comparable_functor {
+  template <typename T>
+  bool operator()() const
+  {
+    return cudf::is_equality_comparable<T, T>();
+  }
+};
+}  // namespace detail
+
+/**
+ * @brief Checks whether `data_type` `type` supports equality comparisons.
+ *
+ * @param type Data_type for comparison.
+ * @return true If `type` supports equality comparisons.
+ * @return false If `type` does not support equality comparisons.
+ */
+inline bool is_equality_comparable(data_type type)
+{
+  return cudf::type_dispatcher(type, detail::unary_equality_comparable_functor{});
+}
+
 /**
  * @brief Indicates whether the type `T` is a numeric type.
  *
diff --git a/cpp/src/groupby/common/utils.hpp b/cpp/src/groupby/common/utils.hpp
index 3da20fb9af3..2804dea576e 100644
--- a/cpp/src/groupby/common/utils.hpp
+++ b/cpp/src/groupby/common/utils.hpp
@@ -1,5 +1,5 @@
 /*
- * Copyright (c) 2019-20, NVIDIA CORPORATION.
+ * Copyright (c) 2019-2021, NVIDIA CORPORATION.
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
diff --git a/cpp/src/groupby/groupby.cu b/cpp/src/groupby/groupby.cu
index 533f193d692..bdaccba38dc 100644
--- a/cpp/src/groupby/groupby.cu
+++ b/cpp/src/groupby/groupby.cu
@@ -27,10 +27,12 @@
 #include <cudf/detail/nvtx/ranges.hpp>
 #include <cudf/dictionary/dictionary_column_view.hpp>
 #include <cudf/groupby.hpp>
+#include <cudf/strings/string_view.hpp>
 #include <cudf/table/table.hpp>
 #include <cudf/table/table_view.hpp>
 #include <cudf/types.hpp>
 #include <cudf/utilities/error.hpp>
+#include <cudf/utilities/traits.hpp>
 #include <structs/utilities.hpp>
 
 #include <rmm/cuda_stream_view.hpp>
@@ -76,6 +78,9 @@ std::pair<std::unique_ptr<table>, std::vector<aggregation_result>> groupby::disp
     // Optionally flatten nested key columns.
     auto [flattened_keys, _, __, ___] =
       flatten_nested_columns(_keys, {}, {}, column_nullability::FORCE);
+    auto is_supported_key_type = [](auto col) { return cudf::is_equality_comparable(col.type()); };
+    CUDF_EXPECTS(std::all_of(flattened_keys.begin(), flattened_keys.end(), is_supported_key_type),
+                 "Unsupported groupby key type does not support equality comparison");
     auto [grouped_keys, results] =
       detail::hash::groupby(flattened_keys, requests, _include_null_keys, stream, mr);
     return std::make_pair(unflatten_nested_columns(std::move(grouped_keys), _keys),
diff --git a/cpp/src/groupby/sort/sort_helper.cu b/cpp/src/groupby/sort/sort_helper.cu
index 69d68f7b6bc..c4905b86ab9 100644
--- a/cpp/src/groupby/sort/sort_helper.cu
+++ b/cpp/src/groupby/sort/sort_helper.cu
@@ -23,8 +23,10 @@
 #include <cudf/detail/iterator.cuh>
 #include <cudf/detail/scatter.hpp>
 #include <cudf/detail/sorting.hpp>
+#include <cudf/strings/string_view.hpp>
 #include <cudf/table/row_operators.cuh>
 #include <cudf/table/table_device_view.cuh>
+#include <cudf/utilities/traits.hpp>
 #include <structs/utilities.hpp>
 
 #include <rmm/cuda_stream_view.hpp>
@@ -102,6 +104,9 @@ sort_groupby_helper::sort_groupby_helper(table_view const& keys,
 
   auto [flattened_keys, _, __, struct_null_vectors] =
     flatten_nested_columns(keys, {}, {}, column_nullability::FORCE);
+  auto is_supported_key_type = [](auto col) { return cudf::is_equality_comparable(col.type()); };
+  CUDF_EXPECTS(std::all_of(flattened_keys.begin(), flattened_keys.end(), is_supported_key_type),
+               "Unsupported groupby key type does not support equality comparison");
   _struct_null_vectors = std::move(struct_null_vectors);
   _keys                = flattened_keys;
 
diff --git a/cpp/tests/CMakeLists.txt b/cpp/tests/CMakeLists.txt
index d9553d463ab..03f7967cee0 100644
--- a/cpp/tests/CMakeLists.txt
+++ b/cpp/tests/CMakeLists.txt
@@ -62,6 +62,7 @@ ConfigureTest(GROUPBY_TEST
     groupby/count_tests.cpp
     groupby/groups_tests.cpp
     groupby/keys_tests.cpp
+    groupby/lists_tests.cpp
     groupby/m2_tests.cpp
     groupby/min_tests.cpp
     groupby/max_scan_tests.cpp
diff --git a/cpp/tests/groupby/lists_tests.cpp b/cpp/tests/groupby/lists_tests.cpp
new file mode 100644
index 00000000000..11b8ffa92b9
--- /dev/null
+++ b/cpp/tests/groupby/lists_tests.cpp
@@ -0,0 +1,69 @@
+/*
+ * Copyright (c) 2021, NVIDIA CORPORATION.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#include <tests/groupby/groupby_test_util.hpp>
+
+#include <cudf_test/base_fixture.hpp>
+#include <cudf_test/column_wrapper.hpp>
+#include <cudf_test/iterator_utilities.hpp>
+#include <cudf_test/type_lists.hpp>
+
+#include <cudf/detail/aggregation/aggregation.hpp>
+
+namespace cudf {
+namespace test {
+
+template <typename V>
+struct groupby_lists_test : public cudf::test::BaseFixture {
+};
+
+TYPED_TEST_SUITE(groupby_lists_test, cudf::test::FixedWidthTypes);
+
+namespace {
+// Checking with a single aggregation, and aggregation column.
+// This test is orthogonal to the aggregation type; it focuses on testing the grouping
+// with LISTS keys.
+auto sum_agg() { return cudf::make_sum_aggregation<groupby_aggregation>(); }
+
+void test_sort_based_sum_agg(column_view const& keys, column_view const& values)
+{
+  test_single_agg(
+    keys, values, keys, values, sum_agg(), force_use_sort_impl::YES, null_policy::INCLUDE);
+}
+
+void test_hash_based_sum_agg(column_view const& keys, column_view const& values)
+{
+  test_single_agg(
+    keys, values, keys, values, sum_agg(), force_use_sort_impl::NO, null_policy::INCLUDE);
+}
+
+}  // namespace
+
+TYPED_TEST(groupby_lists_test, top_level_lists_are_unsupported)
+{
+  // Test that grouping on LISTS columns fails visibly.
+
+  // clang-format off
+  auto keys   = lists_column_wrapper<TypeParam, int32_t> { {1,1},  {2,2},  {3,3},   {1,1},   {2,2} };
+  auto values = fixed_width_column_wrapper<int32_t>      {     0,      1,      2,      3,       4  };
+  // clang-format on
+
+  EXPECT_THROW(test_sort_based_sum_agg(keys, values), cudf::logic_error);
+  EXPECT_THROW(test_hash_based_sum_agg(keys, values), cudf::logic_error);
+}
+
+}  // namespace test
+}  // namespace cudf
diff --git a/cpp/tests/groupby/structs_tests.cpp b/cpp/tests/groupby/structs_tests.cpp
index 00126a4a5a0..3715ba8d17b 100644
--- a/cpp/tests/groupby/structs_tests.cpp
+++ b/cpp/tests/groupby/structs_tests.cpp
@@ -22,8 +22,6 @@
 #include <cudf_test/type_lists.hpp>
 
 #include <cudf/detail/aggregation/aggregation.hpp>
-#include "cudf/aggregation.hpp"
-#include "cudf/types.hpp"
 
 using namespace cudf::test::iterators;
 
@@ -34,7 +32,7 @@ template <typename V>
 struct groupby_structs_test : public cudf::test::BaseFixture {
 };
 
-TYPED_TEST_CASE(groupby_structs_test, cudf::test::FixedWidthTypes);
+TYPED_TEST_SUITE(groupby_structs_test, cudf::test::FixedWidthTypes);
 
 using V       = int32_t;  // Type of Aggregation Column.
 using M0      = int32_t;  // Type of STRUCT's first (i.e. 0th) member.
@@ -79,27 +77,43 @@ void print_agg_results(column_view const& keys, column_view const& vals)
   }
 }
 
-void test_sum_agg(column_view const& keys,
-                  column_view const& values,
-                  column_view const& expected_keys,
-                  column_view const& expected_values)
+void test_sort_based_sum_agg(column_view const& keys,
+                             column_view const& values,
+                             column_view const& expected_keys,
+                             column_view const& expected_values)
 {
   test_single_agg(keys,
                   values,
                   expected_keys,
                   expected_values,
                   sum_agg(),
-                  force_use_sort_impl::NO,
+                  force_use_sort_impl::YES,
                   null_policy::INCLUDE);
+}
+
+void test_hash_based_sum_agg(column_view const& keys,
+                             column_view const& values,
+                             column_view const& expected_keys,
+                             column_view const& expected_values)
+{
   test_single_agg(keys,
                   values,
                   expected_keys,
                   expected_values,
                   sum_agg(),
-                  force_use_sort_impl::YES,
+                  force_use_sort_impl::NO,
                   null_policy::INCLUDE);
 }
 
+void test_sum_agg(column_view const& keys,
+                  column_view const& values,
+                  column_view const& expected_keys,
+                  column_view const& expected_values)
+{
+  test_sort_based_sum_agg(keys, values, expected_keys, expected_values);
+  test_hash_based_sum_agg(keys, values, expected_keys, expected_values);
+}
+
 }  // namespace
 
 TYPED_TEST(groupby_structs_test, basic)
@@ -312,7 +326,8 @@ TYPED_TEST(groupby_structs_test, lists_are_unsupported)
   // clang-format on
   auto keys = structs{{member_0, member_1}};
 
-  EXPECT_THROW(test_sum_agg(keys, values, keys, values), cudf::logic_error);
+  EXPECT_THROW(test_sort_based_sum_agg(keys, values, keys, values), cudf::logic_error);
+  EXPECT_THROW(test_hash_based_sum_agg(keys, values, keys, values), cudf::logic_error);
 }
 
 }  // namespace test