diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index 4d76da8293..d05d2fd3d5 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -2444,17 +2444,25 @@ ReindexTable(RangeVar *relation, int options, bool concurrent)
 									   RangeVarCallbackOwnsTable, NULL);
 
 	if (concurrent)
+	{
 		result = ReindexRelationConcurrently(heapOid, options);
+
+		if (!result)
+			ereport(NOTICE,
+					(errmsg("table \"%s\" has no indexes that can be reindexed concurrently",
+							relation->relname)));
+	}
 	else
+	{
 		result = reindex_relation(heapOid,
 								  REINDEX_REL_PROCESS_TOAST |
 								  REINDEX_REL_CHECK_CONSTRAINTS,
 								  options);
-
-	if (!result)
-		ereport(NOTICE,
-				(errmsg("table \"%s\" has no indexes",
-						relation->relname)));
+		if (!result)
+			ereport(NOTICE,
+					(errmsg("table \"%s\" has no indexes to reindex",
+							relation->relname)));
+	}
 
 	return heapOid;
 }
@@ -2636,7 +2644,6 @@ ReindexMultipleTables(const char *objectName, ReindexObjectType objectKind,
 	foreach(l, relids)
 	{
 		Oid			relid = lfirst_oid(l);
-		bool		result;
 
 		StartTransactionCommand();
 		/* functions in indexes may want a snapshot set */
@@ -2644,11 +2651,13 @@ ReindexMultipleTables(const char *objectName, ReindexObjectType objectKind,
 
 		if (concurrent)
 		{
-			result = ReindexRelationConcurrently(relid, options);
+			(void) ReindexRelationConcurrently(relid, options);
 			/* ReindexRelationConcurrently() does the verbose output */
 		}
 		else
 		{
+			bool		result;
+
 			result = reindex_relation(relid,
 									  REINDEX_REL_PROCESS_TOAST |
 									  REINDEX_REL_CHECK_CONSTRAINTS,
@@ -2675,13 +2684,19 @@ ReindexMultipleTables(const char *objectName, ReindexObjectType objectKind,
  * ReindexRelationConcurrently - process REINDEX CONCURRENTLY for given
  * relation OID
  *
- * The relation can be either an index or a table.  If it is a table, all its
- * valid indexes will be rebuilt, including its associated toast table
- * indexes.  If it is an index, this index itself will be rebuilt.
+ * 'relationOid' can either belong to an index, a table or a materialized
+ * view.  For tables and materialized views, all its indexes will be rebuilt,
+ * excluding invalid indexes and any indexes used in exclusion constraints,
+ * but including its associated toast table indexes.  For indexes, the index
+ * itself will be rebuilt.  If 'relationOid' belongs to a partitioned table
+ * then we issue a warning to mention these are not yet supported.
  *
  * The locks taken on parent tables and involved indexes are kept until the
  * transaction is committed, at which point a session lock is taken on each
  * relation.  Both of these protect against concurrent schema changes.
+ *
+ * Returns true if any indexes have been rebuilt (including toast table's
+ * indexes, when relevant), otherwise returns false.
  */
 static bool
 ReindexRelationConcurrently(Oid relationOid, int options)
diff --git a/src/test/regress/expected/create_index.out b/src/test/regress/expected/create_index.out
index c8bc6be061..c30e6738ba 100644
--- a/src/test/regress/expected/create_index.out
+++ b/src/test/regress/expected/create_index.out
@@ -1944,9 +1944,9 @@ DROP TABLE reindex_verbose;
 CREATE TABLE concur_reindex_tab (c1 int);
 -- REINDEX
 REINDEX TABLE concur_reindex_tab; -- notice
-NOTICE:  table "concur_reindex_tab" has no indexes
+NOTICE:  table "concur_reindex_tab" has no indexes to reindex
 REINDEX TABLE CONCURRENTLY concur_reindex_tab; -- notice
-NOTICE:  table "concur_reindex_tab" has no indexes
+NOTICE:  table "concur_reindex_tab" has no indexes that can be reindexed concurrently
 ALTER TABLE concur_reindex_tab ADD COLUMN c2 text; -- add toast index
 -- Normal index with integer column
 CREATE UNIQUE INDEX concur_reindex_ind1 ON concur_reindex_tab(c1);
@@ -2043,10 +2043,10 @@ ERROR:  REINDEX is not yet implemented for partitioned indexes
 -- REINDEX is a no-op for partitioned tables
 REINDEX TABLE concur_reindex_part_10;
 WARNING:  REINDEX of partitioned tables is not yet implemented, skipping "concur_reindex_part_10"
-NOTICE:  table "concur_reindex_part_10" has no indexes
+NOTICE:  table "concur_reindex_part_10" has no indexes to reindex
 REINDEX TABLE CONCURRENTLY concur_reindex_part_10;
 WARNING:  REINDEX of partitioned tables is not yet implemented, skipping "concur_reindex_part_10"
-NOTICE:  table "concur_reindex_part_10" has no indexes
+NOTICE:  table "concur_reindex_part_10" has no indexes that can be reindexed concurrently
 SELECT relid, parentrelid, level FROM pg_partition_tree('concur_reindex_part_index')
   ORDER BY relid, level;
              relid             |         parentrelid         | level 
@@ -2150,7 +2150,7 @@ DELETE FROM concur_reindex_tab4 WHERE c1 = 1;
 -- The invalid index is not processed when running REINDEX TABLE.
 REINDEX TABLE CONCURRENTLY concur_reindex_tab4;
 WARNING:  cannot reindex invalid index "public.concur_reindex_ind5" concurrently, skipping
-NOTICE:  table "concur_reindex_tab4" has no indexes
+NOTICE:  table "concur_reindex_tab4" has no indexes that can be reindexed concurrently
 \d concur_reindex_tab4
         Table "public.concur_reindex_tab4"
  Column |  Type   | Collation | Nullable | Default