diff -u b/core/includes/bootstrap.inc b/core/includes/bootstrap.inc
--- b/core/includes/bootstrap.inc
+++ b/core/includes/bootstrap.inc
@@ -18,11 +18,14 @@
 use Symfony\Component\DependencyInjection\Exception\ServiceNotFoundException;
 
 /**
- * Minimum supported version of PHP.
- *
- * Updates cannot be run on versions of PHP older than this version.
+ * Minimum allowed version of PHP.
  *
- * The installer exits early on versions of PHP older than this version.
+ * Below this version:
+ * - The installer cannot be run.
+ * - Updates cannot be run.
+ * - Modules and themes cannot be enabled.
+ * - If a site managed to bypass all of the above, then an error is shown in
+ *   the status report and various fatal errors occur on various pages.
  *
  * @see install.php
  *
@@ -32,12 +35,18 @@
 const DRUPAL_MINIMUM_PHP = '5.5.9';
 
 /**
- * Drupal cannot be installed on versions of PHP older than this version.
+ * Minimum supported version of PHP.
+ *
+ * Below this version:
+ * - New sites cannot be installed, except from within tests.
+ * - Updates from previous Drupal versions can be run, but users are warned
+ *   that Drupal no longer supports this PHP version.
+ * - An error is shown in the status report that the PHP version is too old.
  *
  * @todo Move this to an appropriate autoloadable class. See
  *   https://www.drupal.org/project/drupal/issues/2908079
  */
-const DRUPAL_MINIMUM_INSTALL_PHP = '7.0.8';
+const DRUPAL_MINIMUM_SUPPORTED_PHP = '7.0.8';
 
 /**
  * Minimum recommended version of PHP.
diff -u b/core/modules/system/system.install b/core/modules/system/system.install
--- b/core/modules/system/system.install
+++ b/core/modules/system/system.install
@@ -186,30 +186,40 @@
     ];
   }
 
-  if (version_compare($phpversion, DRUPAL_MINIMUM_INSTALL_PHP) < 0) {
+  // Check if the PHP version is below what Drupal supports.
+  if (version_compare($phpversion, DRUPAL_MINIMUM_SUPPORTED_PHP) < 0) {
     $requirements['php']['description'] = t('Your PHP installation is too old. Drupal requires at least PHP %version. It is recommended to upgrade to PHP version %recommended or higher for the best ongoing support. See <a href="http://php.net/supported-versions.php">PHP\'s version support documentation</a> and the <a href=":php_requirements">Drupal 8 PHP requirements handbook page</a> for more information.',
       [
-        '%version' => DRUPAL_MINIMUM_INSTALL_PHP,
+        '%version' => DRUPAL_MINIMUM_SUPPORTED_PHP,
         '%recommended' => DRUPAL_RECOMMENDED_PHP,
         ':php_requirements' => 'https://www.drupal.org/docs/8/system-requirements/php',
       ]
     );
     $requirements['php']['severity'] = REQUIREMENT_ERROR;
 
-    // If PHP is old, it's not safe to continue with the requirements check.
+    // If the PHP version is also below the absolute minimum allowed, it's not
+    // safe to continue with the requirements check.
     if (version_compare($phpversion, DRUPAL_MINIMUM_PHP) < 0) {
       return $requirements;
     }
-    // Only show a warning during updates, so sites running on an older version
-    // of PHP are still able to run them.
+    // Otherwise downgrade the error to a warning during updates. Even if there
+    // are some problems with the site's PHP version, it's still better for the
+    // site to keep its Drupal codebase up to date.
     elseif ($phase === 'update') {
       $requirements['php']['severity'] = REQUIREMENT_WARNING;
     }
-    // Allow test installations of Drupal on older PHP versions.
+    // Since we allow sites with unsupported PHP versions to still run Drupal
+    // updates, we also need to be able to run tests with those PHP versions,
+    // which requires the ability to install test sites. Not all tests are
+    // required to pass on these PHP versions, but we want to monitor which
+    // ones do and don't.
     elseif ($phase === 'install' && drupal_valid_test_ua()) {
       $requirements['php']['severity'] = REQUIREMENT_INFO;
     }
   }
+  // For PHP versions that are still supported but no longer recommended,
+  // inform users of what's recommended, allowing them to take action before it
+  // becomes urgent.
   elseif ($phase === 'runtime' && version_compare($phpversion, DRUPAL_RECOMMENDED_PHP) < 0) {
     $requirements['php']['description'] = t('It is recommended to upgrade to PHP version %recommended or higher for the best ongoing support.  See <a href="http://php.net/supported-versions.php">PHP\'s version support documentation</a> and the <a href=":php_requirements">Drupal 8 PHP requirements handbook page</a> for more information.', ['%recommended' => DRUPAL_RECOMMENDED_PHP, ':php_requirements' => 'https://www.drupal.org/docs/8/system-requirements/php']);
     $requirements['php']['severity'] = REQUIREMENT_INFO;
diff -u b/core/tests/Drupal/Tests/Core/Command/QuickStartTest.php b/core/tests/Drupal/Tests/Core/Command/QuickStartTest.php
--- b/core/tests/Drupal/Tests/Core/Command/QuickStartTest.php
+++ b/core/tests/Drupal/Tests/Core/Command/QuickStartTest.php
@@ -84,7 +84,7 @@
    * Tests the quick-start command.
    */
   public function testQuickStartCommand() {
-    if (version_compare(phpversion(), DRUPAL_MINIMUM_INSTALL_PHP) < 0) {
+    if (version_compare(phpversion(), DRUPAL_MINIMUM_SUPPORTED_PHP) < 0) {
       $this->markTestSkipped();
     }
 
@@ -140,7 +140,7 @@
    * Tests that the installer throws a requirement error on older PHP versions.
    */
   public function testPhpRequirement() {
-    if (version_compare(phpversion(), DRUPAL_MINIMUM_INSTALL_PHP) >= 0) {
+    if (version_compare(phpversion(), DRUPAL_MINIMUM_SUPPORTED_PHP) >= 0) {
       $this->markTestSkipped();
     }
 
@@ -164,7 +164,7 @@
     $error_output = $process->getErrorOutput();
     $this->assertContains('Your PHP installation is too old.', $error_output);
     $this->assertContains('Drupal requires at least PHP', $error_output);
-    $this->assertContains(DRUPAL_MINIMUM_INSTALL_PHP, $error_output);
+    $this->assertContains(DRUPAL_MINIMUM_SUPPORTED_PHP, $error_output);
 
     // Stop the web server.
     $process->stop();
@@ -174,7 +174,7 @@
    * Tests the quick-start commands.
    */
   public function testQuickStartInstallAndServerCommands() {
-    if (version_compare(phpversion(), DRUPAL_MINIMUM_INSTALL_PHP) < 0) {
+    if (version_compare(phpversion(), DRUPAL_MINIMUM_SUPPORTED_PHP) < 0) {
       $this->markTestSkipped();
     }
 
diff -u b/core/tests/Drupal/Tests/RequirementsPageTrait.php b/core/tests/Drupal/Tests/RequirementsPageTrait.php
--- b/core/tests/Drupal/Tests/RequirementsPageTrait.php
+++ b/core/tests/Drupal/Tests/RequirementsPageTrait.php
@@ -12,7 +12,7 @@
    */
   protected function updateRequirementsProblem() {
     // Assert a warning is shown on older test environments.
-    if (version_compare(phpversion(), DRUPAL_MINIMUM_INSTALL_PHP) < 0) {
+    if (version_compare(phpversion(), DRUPAL_MINIMUM_SUPPORTED_PHP) < 0) {
       $this->assertNoText('Errors found');
       $this->assertWarningSummaries(['PHP']);
       $this->clickLink('try again');