diff --git a/core/modules/block/src/Tests/BlockViewBuilderTest.php b/core/modules/block/src/Tests/BlockViewBuilderTest.php
index bd2a986e2d36..ce0d2b421dee 100644
--- a/core/modules/block/src/Tests/BlockViewBuilderTest.php
+++ b/core/modules/block/src/Tests/BlockViewBuilderTest.php
@@ -83,7 +83,7 @@ class BlockViewBuilderTest extends KernelTestBase {
     $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 id="block-test-block1">';
     $expected[] = '  ';
     $expected[] = '    ';
     $expected[] = '      ';
@@ -107,7 +107,7 @@ class BlockViewBuilderTest extends KernelTestBase {
     $entity->save();
     $output = entity_view($entity, 'block');
     $expected = array();
-    $expected[] = '<div id="block-test-block2" class="block block-block-test">';
+    $expected[] = '<div id="block-test-block2">';
     $expected[] = '  ';
     $expected[] = '      <h2>Powered by Bananas</h2>';
     $expected[] = '    ';
diff --git a/core/modules/block/templates/block-list.html.twig b/core/modules/block/templates/block-list.html.twig
index 854d3ce85fe1..bd3c6f753813 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 aa750cb989b5..236b3cfd1b9f 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{{ attributes }}>
   {{ title_prefix }}
   {% if label %}
     <h2{{ title_attributes }}>{{ label }}</h2>
diff --git a/core/themes/classy/templates/block-list.html.twig b/core/themes/classy/templates/block-list.html.twig
new file mode 100644
index 000000000000..854d3ce85fe1
--- /dev/null
+++ b/core/themes/classy/templates/block-list.html.twig
@@ -0,0 +1,23 @@
+{#
+/**
+ * @file
+ * Two column template for the block add/edit form.
+ *
+ * This template will be used when a block edit form specifies 'block_edit_form'
+ * as its #theme callback.  Otherwise, by default, block add/edit forms will be
+ * themed by form.html.twig.
+ *
+ * Available variables:
+ * - form: The block add/edit form.
+ *
+ * @ingroup themeable
+ */
+#}
+<div class="layout-block-list clearfix">
+  <div class="layout-region block-list-primary">
+    {{ form|without('place_blocks') }}
+  </div>
+  <div class="layout-region block-list-secondary">
+    {{ form.place_blocks }}
+  </div>
+</div>
diff --git a/core/themes/classy/templates/block.html.twig b/core/themes/classy/templates/block.html.twig
new file mode 100644
index 000000000000..aa750cb989b5
--- /dev/null
+++ b/core/themes/classy/templates/block.html.twig
@@ -0,0 +1,52 @@
+{#
+/**
+ * @file
+ * Default theme implementation to display a block.
+ *
+ * Available variables:
+ * - plugin_id: The ID of the block implementation.
+ * - label: The configured label of the block if visible.
+ * - configuration: A list of the block's configuration values.
+ *   - label: The configured label for the block.
+ *   - label_display: The display settings for the label.
+ *   - module: The module that provided this block plugin.
+ *   - cache: The cache settings.
+ *   - Block plugin specific settings will also be stored here.
+ * - block - The full block entity.
+ *   - label_hidden: The hidden block title value if the block was
+ *     configured to hide the title ('label' is empty in this case).
+ *   - module: The module that generated the block.
+ *   - delta: An ID for the block, unique within each module.
+ *   - region: The block region embedding the current block.
+ * - content: The content of this block.
+ * - attributes: array of HTML attributes populated by modules, intended to
+ *   be added to the main container tag of this template.
+ *   - id: A valid HTML ID and guaranteed unique.
+ * - title_attributes: Same as attributes, except applied to the main title
+ *   tag that appears in the template.
+ * - title_prefix: Additional output populated by modules, intended to be
+ *   displayed in front of the main title tag that appears in the template.
+ * - title_suffix: Additional output populated by modules, intended to be
+ *   displayed after the main title tag that appears in the template.
+ *
+ * @see template_preprocess_block()
+ *
+ * @ingroup themeable
+ */
+#}
+{%
+  set classes = [
+    'block',
+    'block-' ~ configuration.provider|clean_class,
+  ]
+%}
+<div{{ attributes.addClass(classes) }}>
+  {{ title_prefix }}
+  {% if label %}
+    <h2{{ title_attributes }}>{{ label }}</h2>
+  {% endif %}
+  {{ title_suffix }}
+  {% block content %}
+    {{ content }}
+  {% endblock %}
+</div>