diff --git a/docs/supported_ops.md b/docs/supported_ops.md
index 2eb45dbef5b..db228cb9385 100644
--- a/docs/supported_ops.md
+++ b/docs/supported_ops.md
@@ -354,9 +354,9 @@ Accelerator supports are described below.
 <td>S</td>
 <td><b>NS</b></td>
 <td><b>NS</b></td>
+<td><em>PS* (missing nested BINARY, CALENDAR, MAP, UDT)</em></td>
 <td><b>NS</b></td>
-<td><b>NS</b></td>
-<td><b>NS</b></td>
+<td><em>PS* (missing nested BINARY, CALENDAR, MAP, UDT)</em></td>
 <td><b>NS</b></td>
 </tr>
 <tr>
@@ -538,9 +538,9 @@ Accelerator supports are described below.
 <td>S</td>
 <td><b>NS</b></td>
 <td><b>NS</b></td>
+<td><em>PS* (missing nested BINARY, CALENDAR, MAP, UDT)</em></td>
 <td><b>NS</b></td>
-<td><b>NS</b></td>
-<td><b>NS</b></td>
+<td><em>PS* (missing nested BINARY, CALENDAR, MAP, UDT)</em></td>
 <td><b>NS</b></td>
 </tr>
 <tr>
diff --git a/integration_tests/src/main/python/array_test.py b/integration_tests/src/main/python/array_test.py
index 06c78654a9e..412f0c56ac4 100644
--- a/integration_tests/src/main/python/array_test.py
+++ b/integration_tests/src/main/python/array_test.py
@@ -14,11 +14,9 @@
 
 import pytest
 
-from asserts import assert_gpu_and_cpu_are_equal_collect
+from asserts import assert_gpu_and_cpu_are_equal_collect, assert_gpu_and_cpu_are_equal_sql
 from data_gen import *
-from marks import incompat
 from pyspark.sql.types import *
-import pyspark.sql.functions as f
 
 # Once we support arrays as literals then we can support a[null] and
 # negative indexes for all array gens. When that happens
@@ -55,3 +53,31 @@ def test_make_array(data_gen):
             lambda spark : binary_op_df(spark, data_gen).selectExpr(
                 'array(a, b)',
                 'array(b, a, null, {}, {})'.format(s1, s2)))
+
+
+@pytest.mark.parametrize('data_gen', single_level_array_gens, ids=idfn)
+def test_orderby_array(data_gen):
+    assert_gpu_and_cpu_are_equal_sql(
+        lambda spark : unary_op_df(spark, data_gen),
+        'array_table',
+        'select array_table.a, array_table.a[0] as first_val from array_table order by first_val',
+        conf=allow_negative_scale_of_decimal_conf)
+
+
+@pytest.mark.parametrize('data_gen', [ArrayGen(ArrayGen(short_gen, max_length=10), max_length=10),
+                                      ArrayGen(ArrayGen(string_gen, max_length=10), max_length=10)], ids=idfn)
+def test_orderby_array_of_arrays(data_gen):
+    assert_gpu_and_cpu_are_equal_sql(
+    lambda spark : unary_op_df(spark, data_gen),
+        'array_table',
+        'select array_table.a, array_table.a[0][0] as first_val from array_table order by first_val')
+
+
+@pytest.mark.parametrize('data_gen', [ArrayGen(StructGen([['child0', byte_gen],
+                                                          ['child1', string_gen],
+                                                          ['child2', float_gen]]))], ids=idfn)
+def test_orderby_array_of_structs(data_gen):
+    assert_gpu_and_cpu_are_equal_sql(
+        lambda spark : unary_op_df(spark, data_gen),
+        'array_table',
+        'select array_table.a, array_table.a[0].child0 as first_val from array_table order by first_val')
\ No newline at end of file
diff --git a/integration_tests/src/main/python/struct_test.py b/integration_tests/src/main/python/struct_test.py
index 004550049cd..bde3b4992e4 100644
--- a/integration_tests/src/main/python/struct_test.py
+++ b/integration_tests/src/main/python/struct_test.py
@@ -14,11 +14,9 @@
 
 import pytest
 
-from asserts import assert_gpu_and_cpu_are_equal_collect
+from asserts import assert_gpu_and_cpu_are_equal_collect, assert_gpu_and_cpu_are_equal_sql
 from data_gen import *
-from marks import incompat
 from pyspark.sql.types import *
-import pyspark.sql.functions as f
 
 @pytest.mark.parametrize('data_gen', [StructGen([["first", boolean_gen], ["second", byte_gen], ["third", float_gen]]),
     StructGen([["first", short_gen], ["second", int_gen], ["third", long_gen]]),
@@ -32,6 +30,7 @@ def test_struct_get_item(data_gen):
                 'a.second',
                 'a.third'))
 
+
 @pytest.mark.parametrize('data_gen', all_basic_gens + [decimal_gen_default, decimal_gen_scale_precision], ids=idfn)
 def test_make_struct(data_gen):
     assert_gpu_and_cpu_are_equal_collect(
@@ -39,3 +38,21 @@ def test_make_struct(data_gen):
                 'struct(a, b)',
                 'named_struct("foo", b, "bar", 5, "end", a)'))
 
+
+@pytest.mark.parametrize('data_gen', [StructGen([["first", boolean_gen], ["second", byte_gen], ["third", float_gen]]),
+                                      StructGen([["first", short_gen], ["second", int_gen], ["third", long_gen]]),
+                                      StructGen([["first", long_gen], ["second", long_gen], ["third", long_gen]]),
+                                      StructGen([["first", string_gen], ["second", ArrayGen(string_gen)], ["third", ArrayGen(string_gen)]])], ids=idfn)
+def test_orderby_struct(data_gen):
+    assert_gpu_and_cpu_are_equal_sql(
+        lambda spark : unary_op_df(spark, data_gen),
+        'struct_table',
+        'select struct_table.a, struct_table.a.first as val from struct_table order by val')
+
+
+@pytest.mark.parametrize('data_gen', [StructGen([["first", string_gen], ["second", ArrayGen(string_gen)], ["third", ArrayGen(string_gen)]])], ids=idfn)
+def test_orderby_struct_2(data_gen):
+    assert_gpu_and_cpu_are_equal_sql(
+        lambda spark : unary_op_df(spark, data_gen),
+        'struct_table',
+        'select struct_table.a, struct_table.a.second[0] as val from struct_table order by val')
\ No newline at end of file
diff --git a/sql-plugin/src/main/scala/com/nvidia/spark/rapids/GpuOverrides.scala b/sql-plugin/src/main/scala/com/nvidia/spark/rapids/GpuOverrides.scala
index 841d6ca1e73..dff2c9dc905 100644
--- a/sql-plugin/src/main/scala/com/nvidia/spark/rapids/GpuOverrides.scala
+++ b/sql-plugin/src/main/scala/com/nvidia/spark/rapids/GpuOverrides.scala
@@ -2335,7 +2335,8 @@ object GpuOverrides {
       }),
     exec[ShuffleExchangeExec](
       "The backend for most data being exchanged between processes",
-      ExecChecks(TypeSig.commonCudfTypes + TypeSig.NULL + TypeSig.DECIMAL, TypeSig.all),
+      ExecChecks((TypeSig.commonCudfTypes + TypeSig.NULL + TypeSig.DECIMAL + TypeSig.ARRAY +
+        TypeSig.STRUCT).nested(), TypeSig.all),
       (shuffle, conf, p, r) => new GpuShuffleMeta(shuffle, conf, p, r)),
     exec[UnionExec](
       "The backend for the union operator",
@@ -2386,7 +2387,10 @@ object GpuOverrides {
       (agg, conf, p, r) => new GpuSortAggregateMeta(agg, conf, p, r)),
     exec[SortExec](
       "The backend for the sort operator",
-      ExecChecks(TypeSig.commonCudfTypes + TypeSig.NULL + TypeSig.DECIMAL, TypeSig.all),
+      // The SortOrder TypeSig will govern what types can actually be used as sorting key data type.
+      // The types below are allowed as inputs and outputs.
+      ExecChecks((TypeSig.commonCudfTypes + TypeSig.NULL + TypeSig.DECIMAL + TypeSig.ARRAY +
+        TypeSig.STRUCT).nested(), TypeSig.all),
       (sort, conf, p, r) => new GpuSortMeta(sort, conf, p, r)),
     exec[ExpandExec](
       "The backend for the expand operator",