diff --git a/examples/flutter_gallery/lib/gallery/item.dart b/examples/flutter_gallery/lib/gallery/item.dart
index 2a66be7739f..eef79d39d41 100644
--- a/examples/flutter_gallery/lib/gallery/item.dart
+++ b/examples/flutter_gallery/lib/gallery/item.dart
@@ -109,6 +109,13 @@ List<GalleryItem> _buildGalleryItems() {
       routeName: ChipDemo.routeName,
       buildRoute: (BuildContext context) => new ChipDemo(),
     ),
+    new GalleryItem(
+      title: 'Data tables',
+      subtitle: 'Data tables',
+      category: 'Material Components',
+      routeName: DataTableDemo.routeName,
+      buildRoute: (BuildContext context) => new DataTableDemo(),
+    ),
     new GalleryItem(
       title: 'Date and time pickers',
       subtitle: 'Date and time selection widgets',
diff --git a/packages/flutter/lib/src/material/data_table.dart b/packages/flutter/lib/src/material/data_table.dart
index 8d0f8922d35..06a9a7fa3c3 100644
--- a/packages/flutter/lib/src/material/data_table.dart
+++ b/packages/flutter/lib/src/material/data_table.dart
@@ -411,14 +411,15 @@ class DataTable extends StatelessWidget {
       alignment: numeric ? Alignment.centerRight : AlignmentDirectional.centerStart,
       child: new AnimatedDefaultTextStyle(
         style: new TextStyle(
-          // TODO(ianh): font family should be Roboto; see https://github.com/flutter/flutter/issues/3116
+          // TODO(ianh): font family should match Theme; see https://github.com/flutter/flutter/issues/3116
           fontWeight: FontWeight.w500,
           fontSize: _kHeadingFontSize,
-          height: _kHeadingRowHeight / _kHeadingFontSize,
+          height: math.min(1.0, _kHeadingRowHeight / _kHeadingFontSize),
           color: (Theme.of(context).brightness == Brightness.light)
             ? ((onSort != null && sorted) ? Colors.black87 : Colors.black54)
             : ((onSort != null && sorted) ? Colors.white : Colors.white70),
         ),
+        softWrap: false,
         duration: _kSortArrowAnimationDuration,
         child: label,
       ),
diff --git a/packages/flutter/lib/src/material/material_localizations.dart b/packages/flutter/lib/src/material/material_localizations.dart
index 7b809f48954..481fae87a5b 100644
--- a/packages/flutter/lib/src/material/material_localizations.dart
+++ b/packages/flutter/lib/src/material/material_localizations.dart
@@ -503,7 +503,7 @@ class DefaultMaterialLocalizations implements MaterialLocalizations {
   }
 
   @override
-  String get rowsPerPageTitle => 'Rows per page';
+  String get rowsPerPageTitle => 'Rows per page:';
 
   @override
   String selectedRowCountTitle(int selectedRowCount) {
diff --git a/packages/flutter/lib/src/material/paginated_data_table.dart b/packages/flutter/lib/src/material/paginated_data_table.dart
index 3dcda74063b..370d96eb687 100644
--- a/packages/flutter/lib/src/material/paginated_data_table.dart
+++ b/packages/flutter/lib/src/material/paginated_data_table.dart
@@ -324,7 +324,7 @@ class PaginatedDataTableState extends State<PaginatedDataTable> {
     final List<Widget> footerWidgets = <Widget>[];
     if (widget.onRowsPerPageChanged != null) {
       final List<Widget> availableRowsPerPage = widget.availableRowsPerPage
-        .where((int value) => value <= _rowCount)
+        .where((int value) => (value <= _rowCount || value == widget.rowsPerPage))
         .map<DropdownMenuItem<int>>((int value) {
           return new DropdownMenuItem<int>(
             value: value,
@@ -333,15 +333,22 @@ class PaginatedDataTableState extends State<PaginatedDataTable> {
         })
         .toList();
       footerWidgets.addAll(<Widget>[
+        new Container(width: 14.0), // to match trailing padding in case we overflow and end up scrolling
         new Text(localizations.rowsPerPageTitle),
-        new DropdownButtonHideUnderline(
-          child: new DropdownButton<int>(
-            items: availableRowsPerPage,
-            value: widget.rowsPerPage,
-            onChanged: widget.onRowsPerPageChanged,
-            style: footerTextStyle,
-            iconSize: 24.0
-          )
+        new ConstrainedBox(
+          constraints: const BoxConstraints(minWidth: 64.0), // 40.0 for the text, 24.0 for the icon
+          child: new Align(
+            alignment: AlignmentDirectional.centerEnd,
+            child: new DropdownButtonHideUnderline(
+              child: new DropdownButton<int>(
+                items: availableRowsPerPage,
+                value: widget.rowsPerPage,
+                onChanged: widget.onRowsPerPageChanged,
+                style: footerTextStyle,
+                iconSize: 24.0,
+              ),
+            ),
+          ),
         ),
       ]);
     }
@@ -422,15 +429,18 @@ class PaginatedDataTableState extends State<PaginatedDataTable> {
               ),
               child: new Container(
                 height: 56.0,
-                child: new Row(
-                  mainAxisAlignment: MainAxisAlignment.end,
-                  children: footerWidgets
-                )
-              )
-            )
-          )
-        ]
-      )
+                child: new SingleChildScrollView(
+                  scrollDirection: Axis.horizontal,
+                  reverse: true,
+                  child: new Row(
+                    children: footerWidgets,
+                  ),
+                ),
+              ),
+            ),
+          ),
+        ],
+      ),
     );
   }
 }
diff --git a/packages/flutter/lib/src/painting/text_painter.dart b/packages/flutter/lib/src/painting/text_painter.dart
index f3134034e9a..d80c2102683 100644
--- a/packages/flutter/lib/src/painting/text_painter.dart
+++ b/packages/flutter/lib/src/painting/text_painter.dart
@@ -407,7 +407,7 @@ class TextPainter {
     final int nextCodeUnit = _text.codeUnitAt(offset);
     if (nextCodeUnit == null)
       return null;
-    // TODO(goderbauer): doesn't handle flag emojis (https://github.com/flutter/flutter/issues/13404).
+    // TODO(goderbauer): doesn't handle extended grapheme clusters with more than one Unicode scalar value (https://github.com/flutter/flutter/issues/13404).
     return _isUtf16Surrogate(nextCodeUnit) ? offset + 2 : offset + 1;
   }
 
@@ -417,7 +417,7 @@ class TextPainter {
     final int prevCodeUnit = _text.codeUnitAt(offset - 1);
     if (prevCodeUnit == null)
       return null;
-    // TODO(goderbauer): doesn't handle flag emojis (https://github.com/flutter/flutter/issues/13404).
+    // TODO(goderbauer): doesn't handle extended grapheme clusters with more than one Unicode scalar value (https://github.com/flutter/flutter/issues/13404).
     return _isUtf16Surrogate(prevCodeUnit) ? offset - 2 : offset - 1;
   }
 
diff --git a/packages/flutter/lib/src/rendering/table.dart b/packages/flutter/lib/src/rendering/table.dart
index 1effa3f2b3a..239049b6836 100644
--- a/packages/flutter/lib/src/rendering/table.dart
+++ b/packages/flutter/lib/src/rendering/table.dart
@@ -113,6 +113,9 @@ class IntrinsicColumnWidth extends TableColumnWidth {
 
   @override
   double flex(Iterable<RenderBox> cells) => _flex;
+
+  @override
+  String toString() => '$runtimeType(flex: ${_flex?.toStringAsFixed(1)})';
 }
 
 /// Sizes the column to a specific number of pixels.
diff --git a/packages/flutter/lib/src/widgets/text.dart b/packages/flutter/lib/src/widgets/text.dart
index 9f1202b3dd7..d63f438de32 100644
--- a/packages/flutter/lib/src/widgets/text.dart
+++ b/packages/flutter/lib/src/widgets/text.dart
@@ -144,6 +144,10 @@ class DefaultTextStyle extends InheritedWidget {
   void debugFillProperties(DiagnosticPropertiesBuilder description) {
     super.debugFillProperties(description);
     style?.debugFillProperties(description);
+    description.add(new EnumProperty<TextAlign>('textAlign', textAlign, defaultValue: null));
+    description.add(new FlagProperty('softWrap', value: softWrap, ifTrue: 'wrapping at box width', ifFalse: 'no wrapping except at line break characters', showName: true));
+    description.add(new EnumProperty<TextOverflow>('overflow', overflow, defaultValue: null));
+    description.add(new IntProperty('maxLines', maxLines, defaultValue: null));
   }
 }
 
diff --git a/packages/flutter/test/material/data_table_test.dart b/packages/flutter/test/material/data_table_test.dart
index 08cdfd70f22..456c35a95a9 100644
--- a/packages/flutter/test/material/data_table_test.dart
+++ b/packages/flutter/test/material/data_table_test.dart
@@ -98,4 +98,116 @@ void main() {
     expect(log, <String>['row-selected: KitKat']);
     log.clear();
   });
+
+  testWidgets('DataTable overflow test - header', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      new MaterialApp(
+        home: new Material(
+          child: new DataTable(
+            columns: <DataColumn>[
+              new DataColumn(
+                label: new Text('X' * 2000),
+              ),
+            ],
+            rows: const <DataRow>[
+              const DataRow(
+                cells: const <DataCell>[
+                  const DataCell(
+                    const Text('X'),
+                  ),
+                ],
+              ),
+            ],
+          ),
+        ),
+      ),
+    );
+    expect(tester.renderObject<RenderBox>(find.byType(Text).first).size.width, greaterThan(800.0));
+    expect(tester.renderObject<RenderBox>(find.byType(Row).first).size.width, greaterThan(800.0));
+    expect(tester.takeException(), isNull); // column overflows table, but text doesn't overflow cell
+  });
+
+  testWidgets('DataTable overflow test - header with spaces', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      new MaterialApp(
+        home: new Material(
+          child: new DataTable(
+            columns: <DataColumn>[
+              new DataColumn(
+                label: new Text('X ' * 2000), // has soft wrap points, but they should be ignored
+              ),
+            ],
+            rows: const <DataRow>[
+              const DataRow(
+                cells: const <DataCell>[
+                  const DataCell(
+                    const Text('X'),
+                  ),
+                ],
+              ),
+            ],
+          ),
+        ),
+      ),
+    );
+    expect(tester.renderObject<RenderBox>(find.byType(Text).first).size.width, greaterThan(800.0));
+    expect(tester.renderObject<RenderBox>(find.byType(Row).first).size.width, greaterThan(800.0));
+    expect(tester.takeException(), isNull); // column overflows table, but text doesn't overflow cell
+  }, skip: true); // https://github.com/flutter/flutter/issues/13512
+
+  testWidgets('DataTable overflow test', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      new MaterialApp(
+        home: new Material(
+          child: new DataTable(
+            columns: const <DataColumn>[
+              const DataColumn(
+                label: const Text('X'),
+              ),
+            ],
+            rows: <DataRow>[
+              new DataRow(
+                cells: <DataCell>[
+                  new DataCell(
+                    new Text('X' * 2000),
+                  ),
+                ],
+              ),
+            ],
+          ),
+        ),
+      ),
+    );
+    expect(tester.renderObject<RenderBox>(find.byType(Text).first).size.width, lessThan(800.0));
+    expect(tester.renderObject<RenderBox>(find.byType(Row).first).size.width, greaterThan(800.0));
+    expect(tester.takeException(), isNull); // cell overflows table, but text doesn't overflow cell
+  });
+
+  testWidgets('DataTable overflow test', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      new MaterialApp(
+        home: new Material(
+          child: new DataTable(
+            columns: const <DataColumn>[
+              const DataColumn(
+                label: const Text('X'),
+              ),
+            ],
+            rows: <DataRow>[
+              new DataRow(
+                cells: <DataCell>[
+                  new DataCell(
+                    new Text('X ' * 2000), // wraps
+                  ),
+                ],
+              ),
+            ],
+          ),
+        ),
+      ),
+    );
+    expect(tester.renderObject<RenderBox>(find.byType(Text).first).size.width, lessThan(800.0));
+    expect(tester.renderObject<RenderBox>(find.byType(Row).first).size.width, lessThan(800.0));
+    expect(tester.takeException(), isNull);
+  });
 }
diff --git a/packages/flutter/test/material/paginated_data_table_test.dart b/packages/flutter/test/material/paginated_data_table_test.dart
index 8592801e1cb..19c9e21119b 100644
--- a/packages/flutter/test/material/paginated_data_table_test.dart
+++ b/packages/flutter/test/material/paginated_data_table_test.dart
@@ -192,4 +192,90 @@ void main() {
     expect(log, <String>['action: adjust']);
     log.clear();
   });
+
+  testWidgets('PaginatedDataTable text alignment', (WidgetTester tester) async {
+    await tester.pumpWidget(new MaterialApp(
+      home: new PaginatedDataTable(
+        header: const Text('HEADER'),
+        source: new TestDataSource(),
+        rowsPerPage: 8,
+        availableRowsPerPage: <int>[
+          8, 9,
+        ],
+        onRowsPerPageChanged: (int rowsPerPage) { },
+        columns: <DataColumn>[
+          const DataColumn(label: const Text('COL1')),
+          const DataColumn(label: const Text('COL2')),
+          const DataColumn(label: const Text('COL3')),
+        ],
+      ),
+    ));
+    expect(find.text('Rows per page:'), findsOneWidget);
+    expect(find.text('8'), findsOneWidget);
+    expect(tester.getTopRight(find.text('8')).dx, tester.getTopRight(find.text('Rows per page:')).dx + 40.0); // per spec
+  });
+
+  testWidgets('PaginatedDataTable with large text', (WidgetTester tester) async {
+    final TestDataSource source = new TestDataSource();
+    await tester.pumpWidget(new MaterialApp(
+      home: new MediaQuery(
+        data: const MediaQueryData(
+          textScaleFactor: 20.0,
+        ),
+        child: new PaginatedDataTable(
+          header: const Text('HEADER'),
+          source: source,
+          rowsPerPage: 501,
+          availableRowsPerPage: <int>[ 501 ],
+          onRowsPerPageChanged: (int rowsPerPage) { },
+          columns: <DataColumn>[
+            const DataColumn(label: const Text('COL1')),
+            const DataColumn(label: const Text('COL2')),
+            const DataColumn(label: const Text('COL3')),
+          ],
+        ),
+      ),
+    ));
+    // the column overflows because we're forcing it to 600 pixels high
+    expect(tester.takeException(), contains('A RenderFlex overflowed by'));
+    expect(find.text('Rows per page:'), findsOneWidget);
+    // Test that we will show some options in the drop down even if the lowest option is bigger than the source:
+    assert(501 > source.rowCount);
+    expect(find.text('501'), findsOneWidget);
+    // Test that it fits:
+    expect(tester.getTopRight(find.text('501')).dx, greaterThanOrEqualTo(tester.getTopRight(find.text('Rows per page:')).dx + 40.0));
+  });
+
+  testWidgets('PaginatedDataTable footer scrolls', (WidgetTester tester) async {
+    final TestDataSource source = new TestDataSource();
+    await tester.pumpWidget(new MaterialApp(
+      home: new Align(
+        alignment: Alignment.topLeft,
+        child: new SizedBox(
+          width: 100.0,
+          child: new PaginatedDataTable(
+            header: const Text('HEADER'),
+            source: source,
+            rowsPerPage: 5,
+            availableRowsPerPage: <int>[ 5 ],
+            onRowsPerPageChanged: (int rowsPerPage) { },
+            columns: <DataColumn>[
+              const DataColumn(label: const Text('COL1')),
+              const DataColumn(label: const Text('COL2')),
+              const DataColumn(label: const Text('COL3')),
+            ],
+          ),
+        ),
+      ),
+    ));
+    expect(find.text('Rows per page:'), findsOneWidget);
+    expect(tester.getTopLeft(find.text('Rows per page:')).dx, lessThan(0.0)); // off screen
+    await tester.dragFrom(
+      new Offset(50.0, tester.getTopLeft(find.text('Rows per page:')).dy),
+      const Offset(1000.0, 0.0),
+    );
+    await tester.pump();
+    expect(find.text('Rows per page:'), findsOneWidget);
+    expect(tester.getTopLeft(find.text('Rows per page:')).dx, 18.0); // 14 padding in the footer row, 4 padding from the card
+  });
 }
diff --git a/packages/flutter/test/rendering/table_test.dart b/packages/flutter/test/rendering/table_test.dart
index f564d3224fb..4681912c6a7 100644
--- a/packages/flutter/test/rendering/table_test.dart
+++ b/packages/flutter/test/rendering/table_test.dart
@@ -82,7 +82,7 @@ void main() {
         ' │ parentData: offset=Offset(335.0, 185.0) (can use size)\n'
         ' │ constraints: BoxConstraints(0.0<=w<=800.0, 0.0<=h<=600.0)\n'
         ' │ size: Size(130.0, 230.0)\n'
-        ' │ default column width: IntrinsicColumnWidth\n'
+        ' │ default column width: IntrinsicColumnWidth(flex: null)\n'
         ' │ table size: 5×5\n'
         ' │ column offsets: 0.0, 10.0, 30.0, 130.0, 130.0\n'
         ' │ row offsets: 0.0, 30.0, 30.0, 30.0, 30.0, 230.0\n'