diff --git a/core/lib/Drupal/Core/DrupalKernelInterface.php b/core/lib/Drupal/Core/DrupalKernelInterface.php
index 83d00bd..4e0e15c 100644
--- a/core/lib/Drupal/Core/DrupalKernelInterface.php
+++ b/core/lib/Drupal/Core/DrupalKernelInterface.php
@@ -61,7 +61,7 @@ public function getContainer();
   /**
    * Sets the current container.
    *
-   * Must be called before boot() in order to bootstrap the given container.
+   * Subsequently call static::boot() to bootstrap the container.
    *
    * @param \Symfony\Component\DependencyInjection\ContainerInterface $container
    *   The container to set.
diff --git a/core/tests/Drupal/Tests/AssertLegacyTrait.php b/core/tests/Drupal/Tests/AssertLegacyTrait.php
index 2140895..03e25e7 100644
--- a/core/tests/Drupal/Tests/AssertLegacyTrait.php
+++ b/core/tests/Drupal/Tests/AssertLegacyTrait.php
@@ -12,11 +12,17 @@
  *
  * Protected methods are custom. Public static methods override methods of
  * \PHPUnit_Framework_Assert.
+ *
+ * @deprecated Scheduled for removal in Drupal 9.0.0. Use PHPUnit's native
+ *   assert methods instead.
  */
 trait AssertLegacyTrait {
 
   /**
    * @see \Drupal\simpletest\TestBase::assert()
+   *
+   * @deprecated Scheduled for removal in Drupal 9.0.0. Use self::assertTrue()
+   *   instead.
    */
   protected function assert($actual, $message = '') {
     parent::assertTrue((bool) $actual, $message);
@@ -48,6 +54,9 @@ public static function assertFalse($actual, $message = '') {
 
   /**
    * @see \Drupal\simpletest\TestBase::assertEqual()
+   *
+   * @deprecated Scheduled for removal in Drupal 9.0.0. Use self::assertEquals()
+   *   instead.
    */
   protected function assertEqual($actual, $expected, $message = '') {
     $this->assertEquals($expected, $actual, $message);
@@ -55,6 +64,9 @@ protected function assertEqual($actual, $expected, $message = '') {
 
   /**
    * @see \Drupal\simpletest\TestBase::assertNotEqual()
+   *
+   * @deprecated Scheduled for removal in Drupal 9.0.0. Use
+   *   self::assertNotEquals() instead.
    */
   protected function assertNotEqual($actual, $expected, $message = '') {
     $this->assertNotEquals($expected, $actual, $message);
@@ -62,6 +74,9 @@ protected function assertNotEqual($actual, $expected, $message = '') {
 
   /**
    * @see \Drupal\simpletest\TestBase::assertIdentical()
+   *
+   * @deprecated Scheduled for removal in Drupal 9.0.0. Use self::assertSame()
+   *   instead.
    */
   protected function assertIdentical($actual, $expected, $message = '') {
     $this->assertSame($expected, $actual, $message);
@@ -69,6 +84,9 @@ protected function assertIdentical($actual, $expected, $message = '') {
 
   /**
    * @see \Drupal\simpletest\TestBase::assertNotIdentical()
+   *
+   * @deprecated Scheduled for removal in Drupal 9.0.0. Use
+   *   self::assertNotSame() instead.
    */
   protected function assertNotIdentical($actual, $expected, $message = '') {
     $this->assertNotSame($expected, $actual, $message);
@@ -76,6 +94,9 @@ protected function assertNotIdentical($actual, $expected, $message = '') {
 
   /**
    * @see \Drupal\simpletest\TestBase::assertIdenticalObject()
+   *
+   * @deprecated Scheduled for removal in Drupal 9.0.0. Use self::assertEquals()
+   *   instead.
    */
   protected function assertIdenticalObject($actual, $expected, $message = '') {
     // Note: ::assertSame checks whether its the same object. ::assertEquals
@@ -86,6 +107,9 @@ protected function assertIdenticalObject($actual, $expected, $message = '') {
 
   /**
    * @see \Drupal\simpletest\TestBase::pass()
+   *
+   * @deprecated Scheduled for removal in Drupal 9.0.0. Use self::assertTrue()
+   *   instead.
    */
   protected function pass($message) {
     $this->assertTrue(TRUE, $message);
diff --git a/core/tests/Drupal/Tests/KernelTestBase.php b/core/tests/Drupal/Tests/KernelTestBase.php
index 1266189..97fb006 100644
--- a/core/tests/Drupal/Tests/KernelTestBase.php
+++ b/core/tests/Drupal/Tests/KernelTestBase.php
@@ -61,30 +61,35 @@
   use RandomGeneratorTrait;
 
   /**
-   * Flag to reset any manipulations to global variables between tests.
+   * {@inheritdoc}
    *
-   * Don't change the value, unless you really know what you are doing.
+   * Back-up and restore any global variables that may be changed by tests.
    *
-   * @var bool
+   * @see self::runTestInSeparateProcess
    */
   protected $backupGlobals = TRUE;
 
   /**
    * {@inheritdoc}
+   *
+   * Kernel tests are run in separate processes to prevent collisions between
+   * code that may be loaded by tests.
    */
   protected $runTestInSeparateProcess = TRUE;
 
   /**
-   * Flag to reset all static class properties between tests.
+   * {@inheritdoc}
    *
-   * @var bool
+   * Back-up and restore static class properties that may be changed by tests.
+   *
+   * @see self::runTestInSeparateProcess
    */
   protected $backupStaticAttributes = TRUE;
 
   /**
-   * Contains a few static class properties for performance.
+   * {@inheritdoc}
    *
-   * @var array
+   * Contains a few static class properties for performance.
    */
   protected $backupStaticAttributesBlacklist = array(
     // Ignore static discovery/parser caches to speed up tests.
@@ -99,9 +104,12 @@
   );
 
   /**
-   * If a test runs in a separate process, do not forward any state.
+   * {@inheritdoc}
+   *
+   * Do not forward any global state from the parent process to the processes
+   * that run the actual tests.
    *
-   * @var bool
+   * @see self::runTestInSeparateProcess
    */
   protected $preserveGlobalState = FALSE;