diff -u b/tests/src/Functional/MenuBlockTest.php b/tests/src/Functional/MenuBlockTest.php
--- b/tests/src/Functional/MenuBlockTest.php
+++ b/tests/src/Functional/MenuBlockTest.php
@@ -2,8 +2,6 @@
 
 namespace Drupal\Tests\menu_block\Functional;
 
-use Drupal\block\Entity\Block;
-use Drupal\menu_link_content\Entity\MenuLinkContent;
 use Drupal\Tests\BrowserTestBase;
 
 /**
@@ -26,6 +24,8 @@
 
   /**
    * An administrative user to configure the test environment.
+   *
+   * @var \Drupal\user\Entity\User|false
    */
   protected $adminUser;
 
@@ -36,8 +36,39 @@
    */
   protected $menuLinkManager;
 
+  /**
+   * The block storage.
+   *
+   * @var \Drupal\Core\Entity\EntityStorageInterface
+   */
   protected $blockStorage;
 
+  /**
+   * The block view builder.
+   *
+   * @var \Drupal\Core\Entity\EntityViewBuilderInterface
+   */
+  protected $blockViewBuilder;
+
+  /**
+   * The menu link content storage.
+   *
+   * @var \Drupal\Core\Entity\EntityStorageInterface
+   */
+  protected $menuLinkContentStorage;
+
+  /**
+   * The module handler service.
+   *
+   * @var \Drupal\Core\Extension\ModuleHandlerInterface
+   */
+  protected $moduleHandler;
+
+  /**
+   * An array containing the menu link plugin ids.
+   *
+   * @var array
+   */
   protected $links;
 
   /**
@@ -48,8 +79,12 @@
 
     $this->menuLinkManager = \Drupal::service('plugin.manager.menu.link');
     $this->blockStorage = \Drupal::service('entity_type.manager')
-      ->getStorage('block')
-    ;
+      ->getStorage('block');
+    $this->blockViewBuilder = \Drupal::service('entity_type.manager')
+      ->getViewBuilder('block');
+    $this->menuLinkContentStorage = \Drupal::service('entity_type.manager')
+      ->getStorage('menu_link_content');
+    $this->moduleHandler = \Drupal::moduleHandler();
 
     $this->links = $this->createLinkHierarchy();
 
@@ -62,6 +97,72 @@
   }
 
   /**
+   * Create a simple hierarchy of links.
+   */
+  protected function createLinkHierarchy() {
+    // First remove all the menu links in the menu.
+    $this->menuLinkManager->deleteLinksInMenu('main');
+
+    // Then create a simple link hierarchy:
+    // - parent menu item
+    //   - child-1 menu item
+    //     - child-1-1 menu item
+    //       - child-1-2 menu item
+    //   - child-2 menu item.
+    $base_options = [
+      'provider' => 'menu_block',
+      'menu_name' => 'main',
+    ];
+
+    $parent = $base_options + [
+      'title' => 'parent menu item',
+      'link' => ['uri' => 'internal:/menu-test/hierarchy/parent'],
+    ];
+    /** @var \Drupal\menu_link_content\MenuLinkContentInterface $link */
+    $link = $this->menuLinkContentStorage->create($parent);
+    $link->save();
+    $links['parent'] = $link->getPluginId();
+
+    $child_1 = $base_options + [
+      'title' => 'child-1 menu item',
+      'link' => ['uri' => 'internal:/menu-test/hierarchy/parent/child'],
+      'parent' => $links['parent'],
+    ];
+    $link = $this->menuLinkContentStorage->create($child_1);
+    $link->save();
+    $links['child-1'] = $link->getPluginId();
+
+    $child_1_1 = $base_options + [
+      'title' => 'child-1-1 menu item',
+      'link' => ['uri' => 'internal:/menu-test/hierarchy/parent/child2/child'],
+      'parent' => $links['child-1'],
+    ];
+    $link = $this->menuLinkContentStorage->create($child_1_1);
+    $link->save();
+    $links['child-1-1'] = $link->getPluginId();
+
+    $child_1_2 = $base_options + [
+      'title' => 'child-1-2 menu item',
+      'link' => ['uri' => 'internal:/menu-test/hierarchy/parent/child2/child'],
+      'parent' => $links['child-1'],
+    ];
+    $link = $this->menuLinkContentStorage->create($child_1_2);
+    $link->save();
+    $links['child-1-2'] = $link->getPluginId();
+
+    $child_2 = $base_options + [
+      'title' => 'child-2 menu item',
+      'link' => ['uri' => 'internal:/menu-test/hierarchy/parent/child'],
+      'parent' => $links['parent'],
+    ];
+    $link = $this->menuLinkContentStorage->create($child_2);
+    $link->save();
+    $links['child-2'] = $link->getPluginId();
+
+    return $links;
+  }
+
+  /**
    * Check if all menu block configuration options are available.
    */
   public function testMenuBlockFormDisplay() {
@@ -71,8 +172,7 @@
     $this->assertSession()->pageTextContains('Expand all menu links');
     $this->assertSession()->pageTextContains('Fixed parent item');
     $this->assertSession()
-      ->pageTextContains('Make the initial visibility level follow the active menu item.')
-    ;
+      ->pageTextContains('Make the initial visibility level follow the active menu item.');
     $this->assertSession()->pageTextContains('Theme hook suggestion');
   }
 
@@ -95,7 +195,7 @@
       'region' => 'primary_menu',
     ], 'Save block');
 
-    $block = Block::load($block_id);
+    $block = $this->blockStorage->load($block_id);
     $block_settings = $block->get('settings');
     self::assertSame(2, $block_settings['level']);
     self::assertSame(6, $block_settings['depth']);
@@ -131,7 +231,8 @@
       'settings[level]' => 2,
     ], 'Save block');
 
-    // Check if the menu items of level 2 are visible, but not the parent menu item.
+    // Check if the menu items of level 2 are visible, but not the parent menu
+    // item.
     $this->drupalGet('menu-test/hierarchy/parent');
     $this->assertSession()->pageTextContains('child-1 menu item');
     $this->assertSession()->pageTextContains('child-2 menu item');
@@ -166,7 +267,8 @@
       'settings[depth]' => 2,
     ], 'Save block');
 
-    // Check if the menu items of level 2 are visible, but not the parent menu item.
+    // Check if the menu items of level 2 are visible, but not the parent menu
+    // item.
     $this->drupalGet('menu-test/hierarchy/parent');
     $this->assertSession()->pageTextContains('parent menu item');
     $this->assertSession()->pageTextContains('child-1 menu item');
@@ -177,7 +279,8 @@
       'settings[depth]' => 0,
     ], 'Save block');
 
-    // Check if the menu items of level 2 are visible, but not the parent menu item.
+    // Check if the menu items of level 2 are visible, but not the parent menu
+    // item.
     $this->drupalGet('<front>');
     $this->assertSession()->pageTextContains('parent menu item');
     $this->assertSession()->pageTextContains('child-1 menu item');
@@ -217,6 +320,9 @@
     $this->assertSession()->pageTextNotContains('child-2 menu item');
   }
 
+  /**
+   * Test the menu_block parent option.
+   */
   public function testMenuBlockParent() {
     $block_id = 'main';
     $this->drupalPostForm('admin/structure/block/add/menu_block:main', [
@@ -227,7 +333,6 @@
       'region' => 'primary_menu',
     ], 'Save block');
 
-
     $this->drupalGet('<front>');
     $this->assertSession()->pageTextNotContains('parent menu item');
     $this->assertSession()->pageTextContains('child-1 menu item');
@@ -243,6 +348,9 @@
     $this->assertSession()->pageTextContains('child-1-2 menu item');
   }
 
+  /**
+   * Test the menu_block follow and follow_parent option.
+   */
   public function testMenuBlockFollow() {
     $block_id = 'main';
     $this->drupalPostForm('admin/structure/block/add/menu_block:main', [
@@ -287,68 +395,64 @@
   }
 
   /**
-   * Create a simple hierarchy of links.
+   * Test the menu_block suggestion option.
    */
-  protected function createLinkHierarchy() {
-    // First remove all the menu links in the menu.
-    $this->menuLinkManager->deleteLinksInMenu('main');
+  public function testMenuBlockSuggestion() {
+    $block_id = 'main';
+    $this->drupalPostForm('admin/structure/block/add/menu_block:main', [
+      'id' => $block_id,
+      'settings[label]' => 'Main navigation',
+      'settings[label_display]' => FALSE,
+      'settings[suggestion]' => 'mainnav',
+      'region' => 'primary_menu',
+    ], 'Save block');
 
-    // Then create a simple link hierarchy:
-    // - parent menu item
-    //   - child-1 menu item
-    //      - child-1-1 menu item
-    //      - child-1-2 menu item
-    //   - child-2 menu item
-    $base_options = [
-      'provider' => 'menu_block',
-      'menu_name' => 'main',
+    /** @var \Drupal\block\BlockInterface $block */
+    $block = $this->blockStorage->load($block_id);
+    $plugin = $block->getPlugin();
+
+    // Check theme suggestions for block template.
+    $variables = [];
+    $variables['elements']['#configuration'] = $plugin->getConfiguration();
+    $variables['elements']['#plugin_id'] = $plugin->getPluginId();
+    $variables['elements']['#id'] = $block->id();
+    $variables['elements']['#base_plugin_id'] = $plugin->getBaseId();
+    $variables['elements']['#derivative_plugin_id'] = $plugin->getDerivativeId();
+    $variables['elements']['content'] = [];
+    $suggestions = $this->moduleHandler->invokeAll('theme_suggestions_block', [$variables]);
+
+    $base_theme_hook = 'menu_block';
+    $hooks = [
+      'theme_suggestions',
+      'theme_suggestions_' . $base_theme_hook,
     ];
+    $this->moduleHandler->alter($hooks, $suggestions, $variables, $base_theme_hook);
 
-    $parent = $base_options + [
-        'title' => 'parent menu item',
-        'link' => ['uri' => 'internal:/menu-test/hierarchy/parent'],
-      ];
-    $link = MenuLinkContent::create($parent);
-    $link->save();
-    $links['parent'] = $link->getPluginId();
-
-    $child_1 = $base_options + [
-        'title' => 'child-1 menu item',
-        'link' => ['uri' => 'internal:/menu-test/hierarchy/parent/child'],
-        'parent' => $links['parent'],
-      ];
-    $link = MenuLinkContent::create($child_1);
-    $link->save();
-    $links['child-1'] = $link->getPluginId();
-
-    $child_1_1 = $base_options + [
-        'title' => 'child-1-1 menu item',
-        'link' => ['uri' => 'internal:/menu-test/hierarchy/parent/child2/child'],
-        'parent' => $links['child-1'],
-      ];
-    $link = MenuLinkContent::create($child_1_1);
-    $link->save();
-    $links['child-1-1'] = $link->getPluginId();
-
-    $child_1_2 = $base_options + [
-        'title' => 'child-1-2 menu item',
-        'link' => ['uri' => 'internal:/menu-test/hierarchy/parent/child2/child'],
-        'parent' => $links['child-1'],
-      ];
-    $link = MenuLinkContent::create($child_1_2);
-    $link->save();
-    $links['child-1-2'] = $link->getPluginId();
+    $this->assertSame($suggestions, [
+      'block__menu_block',
+      'block__menu_block',
+      'block__menu_block__main',
+      'block__main',
+      'block__menu_block__mainnav',
+    ], 'Found expected block suggestions.');
 
-    $child_2 = $base_options + [
-        'title' => 'child-2 menu item',
-        'link' => ['uri' => 'internal:/menu-test/hierarchy/parent/child'],
-        'parent' => $links['parent'],
-      ];
-    $link = MenuLinkContent::create($child_2);
-    $link->save();
-    $links['child-2'] = $link->getPluginId();
+    // Check theme suggestions for menu template.
+    $variables = [
+      'menu_name' => 'main',
+      'menu_block_configuration' => $plugin->getConfiguration(),
+    ];
+    $suggestions = $this->moduleHandler->invokeAll('theme_suggestions_menu', [$variables]);
 
-    return $links;
+    $base_theme_hook = 'menu';
+    $hooks = [
+      'theme_suggestions',
+      'theme_suggestions_' . $base_theme_hook,
+    ];
+    $this->moduleHandler->alter($hooks, $suggestions, $variables, $base_theme_hook);
+    $this->assertSame($suggestions, [
+      'menu__main',
+      'menu__mainnav',
+    ], 'Found expected menu suggestions.');
   }
 
 }