diff --git a/core/modules/system/src/Tests/Batch/PageTest.php b/core/modules/system/tests/src/Functional/Batch/PageTest.php
similarity index 76%
rename from core/modules/system/src/Tests/Batch/PageTest.php
rename to core/modules/system/tests/src/Functional/Batch/PageTest.php
index dbdf18c..9692fb8 100644
--- a/core/modules/system/src/Tests/Batch/PageTest.php
+++ b/core/modules/system/tests/src/Functional/Batch/PageTest.php
@@ -1,15 +1,15 @@
 <?php
 
-namespace Drupal\system\Tests\Batch;
+namespace Drupal\Tests\system\Functional\Batch;
 
-use Drupal\simpletest\WebTestBase;
+use Drupal\Tests\BrowserTestBase;
 
 /**
  * Tests the content of the progress page.
  *
  * @group Batch
  */
-class PageTest extends WebTestBase {
+class PageTest extends BrowserTestBase {
 
   /**
    * Modules to enable.
@@ -53,7 +53,7 @@ public function testBatchProgressPageTitle() {
     $this->drupalGet('batch-test/test-title');
     // The stack should contain the title shown on the progress page.
     $this->assertEqual(batch_test_stack(), ['Batch Test'], 'The batch title is shown on the batch page.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
+    $this->assertSession()->pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
   }
 
   /**
@@ -61,14 +61,14 @@ public function testBatchProgressPageTitle() {
    */
   public function testBatchProgressMessages() {
     // Go to the initial step only.
-    $this->maximumMetaRefreshCount = 0;
     $this->drupalGet('batch-test/test-title');
-    $this->assertRaw('<div class="progress__description">Initializing.<br />&nbsp;</div>', 'Initial progress message appears correctly.');
-    $this->assertNoRaw('&amp;nbsp;', 'Initial progress message is not double escaped.');
+    $assertSession = $this->assertSession();
+    $assertSession->responseContains('<div class="progress__description">Initializing.<br />&nbsp;</div>', 'Initial progress message appears correctly.');
+    $assertSession->responseNotContains('&amp;nbsp;', 'Initial progress message is not double escaped.');
+
     // Now also go to the next step.
-    $this->maximumMetaRefreshCount = 1;
     $this->drupalGet('batch-test/test-title');
-    $this->assertRaw('<div class="progress__description">Completed 1 of 1.</div>', 'Progress message for second step appears correctly.');
+    $assertSession->responseContains('<div class="progress__description">Completed 1 of 1.</div>', 'Progress message for second step appears correctly.');
   }
 
 }
diff --git a/core/modules/system/src/Tests/Batch/ProcessingTest.php b/core/modules/system/tests/src/Functional/Batch/ProcessingTest.php
similarity index 81%
rename from core/modules/system/src/Tests/Batch/ProcessingTest.php
rename to core/modules/system/tests/src/Functional/Batch/ProcessingTest.php
index 6b90cc8..409b2c8 100644
--- a/core/modules/system/src/Tests/Batch/ProcessingTest.php
+++ b/core/modules/system/tests/src/Functional/Batch/ProcessingTest.php
@@ -1,16 +1,16 @@
 <?php
 
-namespace Drupal\system\Tests\Batch;
+namespace Drupal\Tests\system\Functional\Batch;
 
 use Drupal\Core\Url;
-use Drupal\simpletest\WebTestBase;
+use Drupal\Tests\BrowserTestBase;
 
 /**
  * Tests batch processing in form and non-form workflow.
  *
  * @group Batch
  */
-class ProcessingTest extends WebTestBase {
+class ProcessingTest extends BrowserTestBase {
 
   /**
    * Modules to enable.
@@ -27,7 +27,8 @@ public function testBatchNoForm() {
     $this->drupalGet('batch-test/no-form');
     $this->assertBatchMessages($this->_resultMessages('batch_1'), 'Batch for step 2 performed successfully.');
     $this->assertEqual(batch_test_stack(), $this->_resultStack('batch_1'), 'Execution order was correct.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
+    $this->assertSession()
+      ->pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
   }
 
   /**
@@ -38,7 +39,8 @@ public function testBatchRedirectFinishedCallback() {
     $this->drupalGet('batch-test/finish-redirect');
     $this->assertBatchMessages($this->_resultMessages('batch_1'), 'Batch for step 2 performed successfully.');
     $this->assertEqual(batch_test_stack(), $this->_resultStack('batch_1'), 'Execution order was correct.');
-    $this->assertText('Test page text.', 'Custom redirection after batch execution displays the correct page.');
+    $this->assertSession()
+      ->pageTextContains('Test page text.', 'Custom redirection after batch execution displays the correct page.');
     $this->assertUrl(Url::fromRoute('test_page_test.test_page'));
   }
 
@@ -46,73 +48,84 @@ public function testBatchRedirectFinishedCallback() {
    * Tests batches defined in a form submit handler.
    */
   public function testBatchForm() {
+    $assertSession = $this->assertSession();
     // Batch 0: no operation.
     $edit = ['batch' => 'batch_0'];
     $this->drupalPostForm('batch-test', $edit, 'Submit');
-    $this->assertNoEscaped('<', 'No escaped markup is present.');
+    $assertSession->assertNoEscaped('<', 'No escaped markup is present.');
     $this->assertBatchMessages($this->_resultMessages('batch_0'), 'Batch with no operation performed successfully.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
+    $assertSession
+      ->pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
 
     // Batch 1: several simple operations.
     $edit = ['batch' => 'batch_1'];
     $this->drupalPostForm('batch-test', $edit, 'Submit');
-    $this->assertNoEscaped('<', 'No escaped markup is present.');
+    $assertSession->assertNoEscaped('<', 'No escaped markup is present.');
     $this->assertBatchMessages($this->_resultMessages('batch_1'), 'Batch with simple operations performed successfully.');
     $this->assertEqual(batch_test_stack(), $this->_resultStack('batch_1'), 'Execution order was correct.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
+    $assertSession
+      ->pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
 
     // Batch 2: one multistep operation.
     $edit = ['batch' => 'batch_2'];
     $this->drupalPostForm('batch-test', $edit, 'Submit');
-    $this->assertNoEscaped('<', 'No escaped markup is present.');
+    $assertSession->assertNoEscaped('<', 'No escaped markup is present.');
     $this->assertBatchMessages($this->_resultMessages('batch_2'), 'Batch with multistep operation performed successfully.');
     $this->assertEqual(batch_test_stack(), $this->_resultStack('batch_2'), 'Execution order was correct.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
+    $assertSession
+      ->pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
 
     // Batch 3: simple + multistep combined.
     $edit = ['batch' => 'batch_3'];
     $this->drupalPostForm('batch-test', $edit, 'Submit');
-    $this->assertNoEscaped('<', 'No escaped markup is present.');
+    $assertSession->assertNoEscaped('<', 'No escaped markup is present.');
     $this->assertBatchMessages($this->_resultMessages('batch_3'), 'Batch with simple and multistep operations performed successfully.');
     $this->assertEqual(batch_test_stack(), $this->_resultStack('batch_3'), 'Execution order was correct.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
+    $assertSession->
+      pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
 
     // Batch 4: nested batch.
     $edit = ['batch' => 'batch_4'];
     $this->drupalPostForm('batch-test', $edit, 'Submit');
-    $this->assertNoEscaped('<', 'No escaped markup is present.');
+    $assertSession->assertNoEscaped('<', 'No escaped markup is present.');
     $this->assertBatchMessages($this->_resultMessages('batch_4'), 'Nested batch performed successfully.');
     $this->assertEqual(batch_test_stack(), $this->_resultStack('batch_4'), 'Execution order was correct.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
+    $assertSession->
+      pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
   }
 
   /**
    * Tests batches defined in a multistep form.
    */
   public function testBatchFormMultistep() {
+    $assertSession = $this->assertSession();
     $this->drupalGet('batch-test/multistep');
     $this->assertNoEscaped('<', 'No escaped markup is present.');
-    $this->assertText('step 1', 'Form is displayed in step 1.');
+    $assertSession->
+      pageTextContains('step 1', 'Form is displayed in step 1.');
 
     // First step triggers batch 1.
     $this->drupalPostForm(NULL, [], 'Submit');
     $this->assertBatchMessages($this->_resultMessages('batch_1'), 'Batch for step 1 performed successfully.');
     $this->assertEqual(batch_test_stack(), $this->_resultStack('batch_1'), 'Execution order was correct.');
-    $this->assertText('step 2', 'Form is displayed in step 2.');
-    $this->assertNoEscaped('<', 'No escaped markup is present.');
+    $assertSession->
+      pageTextContains('step 2', 'Form is displayed in step 2.');
+    $assertSession->assertNoEscaped('<', 'No escaped markup is present.');
 
     // Second step triggers batch 2.
     $this->drupalPostForm(NULL, [], 'Submit');
     $this->assertBatchMessages($this->_resultMessages('batch_2'), 'Batch for step 2 performed successfully.');
     $this->assertEqual(batch_test_stack(), $this->_resultStack('batch_2'), 'Execution order was correct.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
-    $this->assertNoEscaped('<', 'No escaped markup is present.');
+    $assertSession->
+      pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
+    $assertSession->assertNoEscaped('<', 'No escaped markup is present.');
 
     // Extra query arguments will trigger logic that will add them to the
     // redirect URL. Make sure they are persisted.
     $this->drupalGet('batch-test/multistep', ['query' => ['big_tree' => 'small_axe']]);
     $this->drupalPostForm(NULL, [], 'Submit');
-    $this->assertText('step 2', 'Form is displayed in step 2.');
+    $assertSession->
+      pageTextContains('step 2', 'Form is displayed in step 2.');
     $this->assertTrue(strpos($this->getUrl(), 'batch-test/multistep?big_tree=small_axe'), 'Query argument was persisted and another extra argument was added.');
   }
 
@@ -130,7 +143,8 @@ public function testBatchFormMultipleBatches() {
     // The stack contains execution order of batch callbacks and submit
     // handlers and logging of corresponding $form_state->getValues().
     $this->assertEqual(batch_test_stack(), $this->_resultStack('chained', $value), 'Execution order was correct, and $form_state is correctly persisted.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
+    $this->assertSession()->
+      pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
   }
 
   /**
@@ -148,7 +162,8 @@ public function testBatchFormProgrammatic() {
     // The stack contains execution order of batch callbacks and submit
     // handlers and logging of corresponding $form_state->getValues().
     $this->assertEqual(batch_test_stack(), $this->_resultStack('chained', $value), 'Execution order was correct, and $form_state is correctly persisted.');
-    $this->assertText('Got out of a programmatic batched form.', 'Page execution continues normally.');
+    $this->assertSession()->
+      pageTextContains('Got out of a programmatic batched form.', 'Page execution continues normally.');
   }
 
   /**
@@ -172,7 +187,8 @@ public function testBatchLargePercentage() {
     $this->drupalGet('batch-test/large-percentage');
     $this->assertBatchMessages($this->_resultMessages('batch_5'), 'Batch for step 2 performed successfully.');
     $this->assertEqual(batch_test_stack(), $this->_resultStack('batch_5'), 'Execution order was correct.');
-    $this->assertText('Redirection successful.', 'Redirection after batch execution is correct.');
+    $this->assertSession()->
+      pageTextContains('Redirection successful.', 'Redirection after batch execution is correct.');
   }