diff --git a/core/modules/block/src/Tests/BlockSystemBrandingTest.php b/core/modules/block/src/Tests/BlockSystemBrandingTest.php
index 82cff41..679bb12 100644
--- a/core/modules/block/src/Tests/BlockSystemBrandingTest.php
+++ b/core/modules/block/src/Tests/BlockSystemBrandingTest.php
@@ -31,16 +31,16 @@ protected function setUp() {
       ->set('slogan', 'Community plumbing')
       ->save();
     // Add the system branding block to the page.
-    $this->drupalPlaceBlock('system_branding_block', array('region' => 'header', 'id' => 'site-branding'));
+    $this->drupalPlaceBlock('system_branding_block', array('region' => 'header'));
   }
 
   /**
    * Tests system branding block configuration.
    */
   public function testSystemBrandingSettings() {
-    $site_logo_xpath = '//div[@id="block-site-branding"]//a[@class="site-logo"]';
-    $site_name_xpath = '//div[@id="block-site-branding"]//div[@class="site-name"]';
-    $site_slogan_xpath = '//div[@id="block-site-branding"]//div[@class="site-slogan"]';
+    $site_logo_xpath = '//div//a[@class="site-logo"]';
+    $site_name_xpath = '//div//div[@class="site-name"]';
+    $site_slogan_xpath = '//div//div[@class="site-slogan"]';
 
     // Set default block settings.
     $this->drupalGet('');
diff --git a/core/modules/block/src/Tests/BlockViewBuilderTest.php b/core/modules/block/src/Tests/BlockViewBuilderTest.php
index bd2a986..79be90d 100644
--- a/core/modules/block/src/Tests/BlockViewBuilderTest.php
+++ b/core/modules/block/src/Tests/BlockViewBuilderTest.php
@@ -58,7 +58,7 @@ protected function setUp() {
     // Create a block with only required values.
     $this->block = $this->controller->create(array(
       'id' => 'test_block',
-      'theme' => 'stark',
+      'theme' => 'classy',
       'plugin' => 'test_cache',
     ));
     $this->block->save();
@@ -74,7 +74,7 @@ public function testBasicRendering() {
 
     $entity = $this->controller->create(array(
       'id' => 'test_block1',
-      'theme' => 'stark',
+      'theme' => 'classy',
       'plugin' => 'test_html',
     ));
     $entity->save();
@@ -83,7 +83,7 @@ public function testBasicRendering() {
     $entity = Block::load('test_block1');
     $output = entity_view($entity, 'block');
     $expected = array();
-    $expected[] = '<div id="block-test-block1" class="block block-block-test">';
+    $expected[] = '<div>';
     $expected[] = '  ';
     $expected[] = '    ';
     $expected[] = '      ';
@@ -98,7 +98,7 @@ public function testBasicRendering() {
     // Test the rendering of a block with a given title.
     $entity = $this->controller->create(array(
       'id' => 'test_block2',
-      'theme' => 'stark',
+      'theme' => 'classy',
       'plugin' => 'test_html',
       'settings' => array(
         'label' => 'Powered by Bananas',
@@ -107,7 +107,7 @@ public function testBasicRendering() {
     $entity->save();
     $output = entity_view($entity, 'block');
     $expected = array();
-    $expected[] = '<div id="block-test-block2" class="block block-block-test">';
+    $expected[] = '<div>';
     $expected[] = '  ';
     $expected[] = '      <h2>Powered by Bananas</h2>';
     $expected[] = '    ';
@@ -128,7 +128,7 @@ public function testBlockViewBuilderCache() {
     // Create an empty block.
     $this->block = $this->controller->create(array(
       'id' => 'test_block',
-      'theme' => 'stark',
+      'theme' => 'classy',
       'plugin' => 'test_cache',
     ));
     $this->block->save();
diff --git a/core/modules/block/templates/block-list.html.twig b/core/modules/block/templates/block-list.html.twig
index 854d3ce..bd3c6f7 100644
--- a/core/modules/block/templates/block-list.html.twig
+++ b/core/modules/block/templates/block-list.html.twig
@@ -13,11 +13,11 @@
  * @ingroup themeable
  */
 #}
-<div class="layout-block-list clearfix">
-  <div class="layout-region block-list-primary">
+<div>
+  <div>
     {{ form|without('place_blocks') }}
   </div>
-  <div class="layout-region block-list-secondary">
+  <div>
     {{ form.place_blocks }}
   </div>
 </div>
diff --git a/core/modules/block/templates/block.html.twig b/core/modules/block/templates/block.html.twig
index aa750cb..b7a3ff7 100644
--- a/core/modules/block/templates/block.html.twig
+++ b/core/modules/block/templates/block.html.twig
@@ -34,13 +34,7 @@
  * @ingroup themeable
  */
 #}
-{%
-  set classes = [
-    'block',
-    'block-' ~ configuration.provider|clean_class,
-  ]
-%}
-<div{{ attributes.addClass(classes) }}>
+<div>
   {{ title_prefix }}
   {% if label %}
     <h2{{ title_attributes }}>{{ label }}</h2>
diff --git a/core/modules/block/templates/block-list.html.twig b/core/themes/classy/templates/block-list.html.twig
similarity index 100%
copy from core/modules/block/templates/block-list.html.twig
copy to core/themes/classy/templates/block-list.html.twig
diff --git a/core/modules/block/templates/block.html.twig b/core/themes/classy/templates/block.html.twig
similarity index 100%
copy from core/modules/block/templates/block.html.twig
copy to core/themes/classy/templates/block.html.twig