diff --git a/core/modules/contact/src/Tests/ContactPersonalTest.php b/core/modules/contact/src/Tests/ContactPersonalTest.php
index 936aed5..40be162 100644
--- a/core/modules/contact/src/Tests/ContactPersonalTest.php
+++ b/core/modules/contact/src/Tests/ContactPersonalTest.php
@@ -1,11 +1,13 @@
 <?php
 
-namespace Drupal\contact\Tests;
+namespace Drupal\Tests\contact\Functional;
 
 use Drupal\Component\Utility\SafeMarkup;
 use Drupal\Component\Render\PlainTextOutput;
 use Drupal\Core\Session\AccountInterface;
-use Drupal\simpletest\WebTestBase;
+use Drupal\Core\Test\AssertMailTrait;
+use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\BrowserTestBase;
 use Drupal\user\RoleInterface;
 
 /**
@@ -13,7 +15,10 @@
  *
  * @group contact
  */
-class ContactPersonalTest extends WebTestBase {
+class ContactPersonalTest extends BrowserTestBase {
+
+  use AssertMailTrait;
+  use AssertPageCacheContextsAndTagsTrait;
 
   /**
    * Modules to enable.
@@ -67,7 +72,7 @@ function testSendPersonalContactMessage() {
     $this->drupalGet('user/' . $this->contactUser->id() . '/contact');
     $this->assertEscaped($mail);
     $message = $this->submitPersonalContact($this->contactUser);
-    $mails = $this->drupalGetMails();
+    $mails = $this->getMails();
     $this->assertEqual(1, count($mails));
     $mail = $mails[0];
     $this->assertEqual($mail['to'], $this->contactUser->getEmail());
diff --git a/core/modules/contact/src/Tests/ContactSitewideTest.php b/core/modules/contact/src/Tests/ContactSitewideTest.php
index ffc2e90..f3db002 100644
--- a/core/modules/contact/src/Tests/ContactSitewideTest.php
+++ b/core/modules/contact/src/Tests/ContactSitewideTest.php
@@ -1,13 +1,14 @@
 <?php
 
-namespace Drupal\contact\Tests;
+namespace Drupal\Tests\contact\Functional;
 
 use Drupal\Component\Utility\Unicode;
 use Drupal\contact\Entity\ContactForm;
 use Drupal\Core\Mail\MailFormatHelper;
+use Drupal\Core\Test\AssertMailTrait;
 use Drupal\Core\Url;
 use Drupal\field_ui\Tests\FieldUiTestTrait;
-use Drupal\simpletest\WebTestBase;
+use Drupal\Tests\BrowserTestBase;
 use Drupal\Core\Entity\EntityTypeInterface;
 use Drupal\user\RoleInterface;
 
@@ -18,9 +19,10 @@
  *
  * @group contact
  */
-class ContactSitewideTest extends WebTestBase {
+class ContactSitewideTest extends BrowserTestBase {
 
   use FieldUiTestTrait;
+  use AssertMailTrait;
 
   /**
    * Modules to enable.
@@ -266,8 +268,8 @@ function testSiteWideContact() {
 
     // Find out in which row the form we want to add a field to is.
     $i = 0;
-    foreach ($this->xpath('//table/tbody/tr') as $row) {
-      if (((string) $row->td[0]->a) == $label) {
+    foreach ($this->xpath('//table/tbody/tr/td[1]/a') as $row_link) {
+      if ($row_link->getText() == $label) {
         break;
       }
       $i++;
@@ -299,7 +301,7 @@ function testSiteWideContact() {
       $field_name . '[0][value]' => $this->randomMachineName(),
     );
     $this->drupalPostForm(NULL, $edit, t('Send message'));
-    $mails = $this->drupalGetMails();
+    $mails = $this->getMails();
     $mail = array_pop($mails);
     $this->assertEqual($mail['subject'], t('[@label] @subject', array('@label' => $label, '@subject' => $edit['subject[0][value]'])));
     $this->assertTrue(strpos($mail['body'], $field_label));
@@ -377,7 +379,7 @@ function testAutoReply() {
     $this->submitContact($this->randomMachineName(16), $email, $subject, 'foo', $this->randomString(128));
 
     // We are testing the auto-reply, so there should be one email going to the sender.
-    $captured_emails = $this->drupalGetMails(array('id' => 'contact_page_autoreply', 'to' => $email));
+    $captured_emails = $this->getMails(array('id' => 'contact_page_autoreply', 'to' => $email));
     $this->assertEqual(count($captured_emails), 1);
     $this->assertEqual(trim($captured_emails[0]['body']), trim(MailFormatHelper::htmlToText($foo_autoreply)));
 
@@ -386,14 +388,14 @@ function testAutoReply() {
     $this->submitContact($this->randomMachineName(16), $email, $this->randomString(64), 'bar', $this->randomString(128));
 
     // Auto-reply for form 'bar' should result in one auto-reply email to the sender.
-    $captured_emails = $this->drupalGetMails(array('id' => 'contact_page_autoreply', 'to' => $email));
+    $captured_emails = $this->getMails(array('id' => 'contact_page_autoreply', 'to' => $email));
     $this->assertEqual(count($captured_emails), 1);
     $this->assertEqual(trim($captured_emails[0]['body']), trim(MailFormatHelper::htmlToText($bar_autoreply)));
 
     // Verify that no auto-reply is sent when the auto-reply field is left blank.
     $email = $this->randomMachineName(32) . '@example.com';
     $this->submitContact($this->randomMachineName(16), $email, $this->randomString(64), 'no_autoreply', $this->randomString(128));
-    $captured_emails = $this->drupalGetMails(array('id' => 'contact_page_autoreply', 'to' => $email));
+    $captured_emails = $this->getMails(array('id' => 'contact_page_autoreply', 'to' => $email));
     $this->assertEqual(count($captured_emails), 0);
 
     // Verify that the current error message doesn't show, that the auto-reply
diff --git a/core/modules/contact/src/Tests/ContactStorageTest.php b/core/modules/contact/src/Tests/ContactStorageTest.php
index ad0e8d4..f32233a 100644
--- a/core/modules/contact/src/Tests/ContactStorageTest.php
+++ b/core/modules/contact/src/Tests/ContactStorageTest.php
@@ -1,6 +1,6 @@
 <?php
 
-namespace Drupal\contact\Tests;
+namespace Drupal\Tests\contact\Functional;
 
 use Drupal\Component\Utility\Unicode;
 use Drupal\contact\Entity\Message;
diff --git a/core/tests/Drupal/FunctionalTests/BrowserTestBaseTest.php b/core/tests/Drupal/FunctionalTests/BrowserTestBaseTest.php
index 25d1c70..9c3ab9b 100644
--- a/core/tests/Drupal/FunctionalTests/BrowserTestBaseTest.php
+++ b/core/tests/Drupal/FunctionalTests/BrowserTestBaseTest.php
@@ -36,11 +36,19 @@ public function testGoTo() {
 
     // Test page contains some text.
     $this->assertSession()->pageTextContains('Test page text.');
+    // Make sure CSS <style> content is not considered as part of the page text.
+    $this->assertSession()->pageTextNotContains('@import');
+    // Make sure JS setting values are not part of the page text.
+    $this->assertSession()->pageTextNotContains('"baseUrl"');
 
     // Check that returned plain text is correct.
     $text = $this->getTextContent();
     $this->assertContains('Test page text.', $text);
     $this->assertNotContains('</html>', $text);
+    // No CSS styles in the plain text response.
+    $this->assertNotContains('@import', $text);
+    // No Drupal JS settings in the plain text response.
+    $this->assertNotContains('"baseUrl"', $text);
 
     // Response includes cache tags that we can assert.
     $this->assertSession()->responseHeaderEquals('X-Drupal-Cache-Tags', 'http_response rendered');
@@ -185,4 +193,22 @@ public function testInstall() {
     $this->assertTrue(file_exists($htaccess_filename), "$htaccess_filename exists");
   }
 
+  /**
+   * Tests that legacy assertions work.
+   */
+  public function testAssertions() {
+    $account = $this->drupalCreateUser(['administer users'], 'test');
+    $this->drupalLogin($account);
+
+    $this->drupalGet('admin/people');
+    $this->assertFieldByXpath('//table/tbody/tr[2]/td[1]/span', $account->getAccountName());
+
+    $this->drupalGet('user/' . $account->id() . '/edit');
+    $this->assertFieldByXpath("//input[@id = 'edit-name']", $account->getAccountName());
+    $this->assertFieldByXpath("//select[@id = 'edit-timezone--2']", 'Australia/Sydney');
+
+    $this->assertNoFieldByXPath('//notexisting');
+    $this->assertNoFieldByXpath("//input[@id = 'edit-name']", 'wrong value');
+  }
+
 }
diff --git a/core/tests/Drupal/Tests/Core/Assert/AssertLegacyTraitTest.php b/core/tests/Drupal/Tests/Core/Assert/AssertLegacyTraitTest.php
index 00dbdf5..fb15bdb 100644
--- a/core/tests/Drupal/Tests/Core/Assert/AssertLegacyTraitTest.php
+++ b/core/tests/Drupal/Tests/Core/Assert/AssertLegacyTraitTest.php
@@ -6,6 +6,7 @@
 use Behat\Mink\Element\NodeElement;
 use Behat\Mink\Session;
 use Drupal\Component\Render\MarkupInterface;
+use Drupal\Component\Utility\Html;
 use Drupal\FunctionalTests\AssertLegacyTrait;
 use Drupal\Tests\UnitTestCase;
 use Drupal\Tests\WebAssert;
@@ -154,6 +155,52 @@ public function testAssertOptionSelectedFail() {
   }
 
   /**
+   * @covers ::assertText
+   */
+  public function testAssertText() {
+    $dangerous = 'Bad html <script>alert(123);</script>';
+    $sanitized = Html::escape($dangerous);
+
+    $this->session
+      ->getResponseHeader('Content-type')
+      ->willReturn('text/html');
+    $this->webAssert
+      ->pageTextContains($sanitized)
+      ->shouldNotBeCalled();
+    $this->webAssert
+      ->pageTextContains($dangerous)
+      ->shouldBeCalled();
+
+    // The legacy ::assertText() returns nothing and calls no PHPUnit assertion,
+    // thus we need a real assertion. If ::assertText() fails, then it will
+    // return the exception and this test will fail.
+    $this->assertNull($this->assertText($sanitized));
+  }
+
+  /**
+   * @covers ::assertNoText
+   */
+  public function testAssertNoText() {
+    $dangerous = 'Bad html <script>alert(123);</script>';
+    $sanitized = Html::escape($dangerous);
+
+    $this->session
+      ->getResponseHeader('Content-type')
+      ->willReturn('text/html');
+    $this->webAssert
+      ->pageTextNotContains($dangerous)
+      ->shouldBeCalled();
+    $this->webAssert
+      ->pageTextNotContains($sanitized)
+      ->shouldNotBeCalled();
+
+    // The legacy ::assertNoText() returns nothing and calls no PHPUnit
+    // assertion, thus we need a real assertion. If ::assertText() fails, then
+    // it will return the exception and this test will fail.
+    $this->assertNull($this->assertNoText($sanitized));
+  }
+
+  /**
    * Returns a mocked behat session object.
    *
    * @return \Behat\Mink\Session
diff --git a/core/tests/Drupal/Tests/DocumentElement.php b/core/tests/Drupal/Tests/DocumentElement.php
new file mode 100644
index 0000000..323bde2
--- /dev/null
+++ b/core/tests/Drupal/Tests/DocumentElement.php
@@ -0,0 +1,46 @@
+<?php
+
+namespace Drupal\Tests;
+
+use DOMDocument;
+use Behat\Mink\Element\DocumentElement as MinkDocumentElement;
+
+/**
+ * Overrides the Mink document to better handle page text.
+ */
+class DocumentElement extends MinkDocumentElement {
+
+  /**
+   * {@inheritdoc}
+   */
+  public function getText() {
+    $raw_content = $this->getContent();
+    $dom = new DOMDocument();
+    // Suppress libxml warnings when loading HTML 5 content.
+    @$dom->loadHTML($raw_content);
+    // Collect DOM elements to be removed because DOMNodeList does not allow us
+    // to remove them directly when iterating over it.
+    $remove = [];
+
+    // Remove all JS script tags, they must never be part of the plain text
+    // content.
+    $scripts = $dom->getElementsByTagName('script');
+    foreach ($scripts as $script) {
+      $remove[] = $script;
+    }
+
+    // Remove all CSS style tags, they must never be part of the plain text
+    // content.
+    $styles = $dom->getElementsByTagName('style');
+    foreach ($styles as $style) {
+      $remove[] = $style;
+    }
+
+    foreach ($remove as $item) {
+      $item->parentNode->removeChild($item);
+    }
+
+    return $dom->textContent;
+  }
+
+}
diff --git a/core/tests/Drupal/Tests/Session.php b/core/tests/Drupal/Tests/Session.php
new file mode 100644
index 0000000..331fa68
--- /dev/null
+++ b/core/tests/Drupal/Tests/Session.php
@@ -0,0 +1,43 @@
+<?php
+
+namespace Drupal\Tests;
+
+use Behat\Mink\Session as MinkSession;
+use Behat\Mink\Driver\DriverInterface;
+use Behat\Mink\Selector\SelectorsHandler;
+
+/**
+ * Overrides the Mink session to better handle page text.
+ */
+class Session extends MinkSession {
+
+  /**
+   * The page document.
+   *
+   * The variable on the parent class is private, so we need to define it again
+   * here.
+   *
+   * @var \Drupal\Tests\DocumentElement
+   */
+  protected $page;
+
+  /**
+   * {@inheritdoc}
+   */
+  public function __construct(DriverInterface $driver, SelectorsHandler $selectorsHandler = NULL) {
+      parent::__construct($driver, $selectorsHandler);
+
+      // Use our own document class.
+      $this->page = new DocumentElement($this);
+  }
+
+  /**
+   * {@inheirtdoc}
+   */
+  public function getPage() {
+    // The variable on the parent class is private, so we need to override this
+    // method.
+    return $this->page;
+  }
+
+}
diff --git a/core/tests/Drupal/Tests/WebAssert.php b/core/tests/Drupal/Tests/WebAssert.php
index a6cb5b5..179ae4c 100644
--- a/core/tests/Drupal/Tests/WebAssert.php
+++ b/core/tests/Drupal/Tests/WebAssert.php
@@ -6,7 +6,6 @@
 use Behat\Mink\WebAssert as MinkWebAssert;
 use Behat\Mink\Element\TraversableElement;
 use Behat\Mink\Exception\ElementNotFoundException;
-use Behat\Mink\Session;
 use Drupal\Component\Utility\Html;
 use Drupal\Core\Url;