diff -u b/core/modules/block/tests/src/Functional/AssertBlockAppearsTrait.php b/core/modules/block/tests/src/Functional/AssertBlockAppearsTrait.php
--- b/core/modules/block/tests/src/Functional/AssertBlockAppearsTrait.php
+++ b/core/modules/block/tests/src/Functional/AssertBlockAppearsTrait.php
@@ -3,6 +3,7 @@
 namespace Drupal\Tests\block\Functional;
 
 use Drupal\block\Entity\Block;
+use Drupal\Component\Render\FormattableMarkup;
 
 /**
  * Provides test assertions for testing block appearance.
@@ -19,7 +20,7 @@
    */
   protected function assertBlockAppears(Block $block) {
     $result = $this->findBlockInstance($block);
-    $this->assertTrue(!empty($result), format_string('Ensure the block @id appears on the page', ['@id' => $block->id()]));
+    $this->assertTrue(!empty($result), new FormattableMarkup('Ensure the block @id appears on the page', ['@id' => $block->id()]));
   }
 
   /**
@@ -30,7 +31,7 @@
    */
   protected function assertNoBlockAppears(Block $block) {
     $result = $this->findBlockInstance($block);
-    $this->assertFalse(!empty($result), format_string('Ensure the block @id does not appear on the page', ['@id' => $block->id()]));
+    $this->assertFalse(!empty($result), new FormattableMarkup('Ensure the block @id does not appear on the page', ['@id' => $block->id()]));
   }
 
   /**
@@ -49 +50 @@
-}
\ No newline at end of file
+}
diff -u b/core/modules/block/tests/src/Functional/BlockTest.php b/core/modules/block/tests/src/Functional/BlockTest.php
--- b/core/modules/block/tests/src/Functional/BlockTest.php
+++ b/core/modules/block/tests/src/Functional/BlockTest.php
@@ -261,7 +261,7 @@
       $theme_settings->set('default', $theme)->save();
       $this->drupalGet('');
       $elements = $this->xpath('//div[@id = :id]', [':id' => Html::getUniqueId('block-' . $block['id'])]);
-      $this->assertNotEmpty($elements, 'The block was found.');
+      $this->assertTrue(!empty($elements), 'The block was found.');
     }
   }
 
diff -u b/core/modules/block/tests/src/Functional/BlockTestBase.php b/core/modules/block/src/Tests/BlockTestBase.php
--- b/core/modules/block/tests/src/Functional/BlockTestBase.php
+++ b/core/modules/block/src/Tests/BlockTestBase.php
@@ -1,14 +1,21 @@
 <?php
 
-namespace Drupal\Tests\block\Functional;
+namespace Drupal\block\Tests;
 
+@trigger_error(__NAMESPACE__ . '\BlockTestBase is deprecated in Drupal 8.5.0 and will be removed before Drupal 9.0.0. Instead, use \Drupal\Tests\block\Functional\BlockTestBase, see https://www.drupal.org/node/2901823.', E_USER_DEPRECATED);
+
+use Drupal\simpletest\WebTestBase;
 use Drupal\filter\Entity\FilterFormat;
-use Drupal\Tests\BrowserTestBase;
 
 /**
  * Provides setup and helper methods for block module tests.
+ *
+ * @deprecated in Drupal 8.5.0 and will be removed before Drupal 9.0.0.
+ *   Use \Drupal\Tests\block\Functional\BlockTestBase.
+ *
+ * @see https://www.drupal.org/node/2901823
  */
-abstract class BlockTestBase extends BrowserTestBase {
+abstract class BlockTestBase extends WebTestBase {
 
   /**
    * Modules to install.
@@ -31,9 +38,6 @@
    */
   protected $adminUser;
 
-  /**
-   * {@inheritdoc}
-   */
   protected function setUp() {
     parent::setUp();
 
diff -u b/core/modules/block/tests/src/Functional/BlockUiTest.php b/core/modules/block/tests/src/Functional/BlockUiTest.php
--- b/core/modules/block/tests/src/Functional/BlockUiTest.php
+++ b/core/modules/block/tests/src/Functional/BlockUiTest.php
@@ -99,7 +99,7 @@
     $this->drupalGet('admin/structure/block');
     // Look for the blocks table.
     $blocks_table = $this->xpath("//table[@id='blocks']");
-    $this->assertNotEmpty($blocks_table, 'The blocks table is being rendered.');
+    $this->assertTrue(!empty($blocks_table), 'The blocks table is being rendered.');
     // Look for test blocks in the table.
     foreach ($this->blockValues as $delta => $values) {
       $block = $this->blocks[$delta];
@@ -134,7 +134,7 @@
     $this->drupalPlaceBlock('system_powered_by_block', ['region' => 'header', 'id' => 'header']);
     $this->drupalGet('admin/structure/block');
     $element = $this->xpath('//tr[contains(@class, :class)]', [':class' => 'region-title-header']);
-    $this->assertNotEmpty($element);
+    $this->assertTrue(!empty($element));
 
     // Ensure hidden themes do not appear in the UI. Enable another non base
     // theme and place the local tasks block.
@@ -173,7 +173,7 @@
     $this->drupalGet('admin/structure/block');
     $this->clickLink('Place block');
     $elements = $this->xpath($pattern, $arguments);
-    $this->assertNotEmpty($elements, 'The test block appears in the category for its module.');
+    $this->assertTrue(!empty($elements), 'The test block appears in the category for its module.');
 
     // Trigger the custom category addition in block_test_block_alter().
     $this->container->get('state')->set('block_test_info_alter', TRUE);
@@ -183,7 +183,7 @@
     $this->clickLink('Place block');
     $arguments[':category'] = 'Custom category';
     $elements = $this->xpath($pattern, $arguments);
-    $this->assertNotEmpty($elements, 'The test block appears in a custom category controlled by block_test_block_alter().');
+    $this->assertTrue(!empty($elements), 'The test block appears in a custom category controlled by block_test_block_alter().');
   }
 
   /**
@@ -199,10 +199,10 @@
     $this->drupalGet('admin/structure/block');
     $this->clickLink('Place block');
     $elements = $this->xpath('//tr[.//td/div[text()=:text] and .//td[text()=:category] and .//td//a[contains(@href, :href)]]', $arguments);
-    $this->assertEmpty($elements, 'The context-aware test block does not appear.');
+    $this->assertTrue(empty($elements), 'The context-aware test block does not appear.');
 
     $definition = \Drupal::service('plugin.manager.block')->getDefinition('test_context_aware_unsatisfied');
-    $this->assertNotEmpty($definition, 'The context-aware test block does not exist.');
+    $this->assertTrue(!empty($definition), 'The context-aware test block does not exist.');
   }
 
   /**
@@ -225,9 +225,9 @@
     $this->drupalGet('admin/structure/block');
     $this->clickLink('Place block');
     $elements = $this->xpath($pattern, $arguments);
-    $this->assertNotEmpty($elements, 'The context-aware test block appears.');
+    $this->assertTrue(!empty($elements), 'The context-aware test block appears.');
     $definition = \Drupal::service('plugin.manager.block')->getDefinition('test_context_aware');
-    $this->assertNotEmpty($definition, 'The context-aware test block exists.');
+    $this->assertTrue(!empty($definition), 'The context-aware test block exists.');
     $edit = [
       'region' => 'content',
       'settings[context_mapping][user]' => '@block_test.multiple_static_context:userB',