src/EntityEmbedDisplay/EntityEmbedDisplayBase.php       | 12 +++++++++++-
 src/EntityEmbedDisplay/EntityEmbedDisplayInterface.php  |  4 ++--
 .../FieldFormatterEntityEmbedDisplayBase.php            |  9 +++++----
 .../EntityEmbedDisplay/ImageFieldFormatter.php          | 17 ++++++++++++-----
 4 files changed, 30 insertions(+), 12 deletions(-)

diff --git a/src/EntityEmbedDisplay/EntityEmbedDisplayBase.php b/src/EntityEmbedDisplay/EntityEmbedDisplayBase.php
index 314b142..9f1b644 100644
--- a/src/EntityEmbedDisplay/EntityEmbedDisplayBase.php
+++ b/src/EntityEmbedDisplay/EntityEmbedDisplayBase.php
@@ -3,6 +3,7 @@
 namespace Drupal\entity_embed\EntityEmbedDisplay;
 
 use Drupal\Component\Utility\NestedArray;
+use Drupal\Core\Access\AccessResult;
 use Drupal\Core\Entity\EntityManagerInterface;
 use Drupal\Core\Form\FormStateInterface;
 use Drupal\Core\Language\LanguageInterface;
@@ -69,7 +70,9 @@ abstract class EntityEmbedDisplayBase extends PluginBase implements ContainerFac
   public function access(AccountInterface $account = NULL) {
     // Check that the plugin's registered entity types matches the current
     // entity type.
-    return $this->isValidEntityType();
+    return AccessResult::allowedIf($this->isValidEntityType())
+      // @see \Drupal\Core\Entity\EntityTypeManager
+      ->addCacheTags(['entity_types']);
   }
 
   /**
@@ -245,6 +248,13 @@ abstract class EntityEmbedDisplayBase extends PluginBase implements ContainerFac
   /**
    * Gets the entity from the current context.
    *
+   * @todo Where doe sthis come from? The value must come from somewhere, yet
+   * this does not implement any context-related interfaces. This is an *input*,
+   * so we need cache contexts and possibly cache tags to reflect where this
+   * came from. We need that for *everything* that this class does that relies
+   * on this, plus any of its subclasses. Right now, this is effectively a
+   * global that breaks cacheability metadata.
+   *
    * @return \Drupal\Core\Entity\EntityInterface
    */
   public function getEntityFromContext() {
diff --git a/src/EntityEmbedDisplay/EntityEmbedDisplayInterface.php b/src/EntityEmbedDisplay/EntityEmbedDisplayInterface.php
index 2284444..6e9e6af 100644
--- a/src/EntityEmbedDisplay/EntityEmbedDisplayInterface.php
+++ b/src/EntityEmbedDisplay/EntityEmbedDisplayInterface.php
@@ -58,8 +58,8 @@ interface EntityEmbedDisplayInterface extends ConfigurablePluginInterface, Plugi
    *   (optional) The user for which to check access, or NULL to check access
    *   for the current user. Defaults to NULL.
    *
-   * @return bool
-   *   TRUE if this Entity Embed Display plugin can be used, or FALSE otherwise.
+   * @return \Drupal\Core\Access\AccessResultInterface
+   *   The access result.
    */
   public function access(AccountInterface $account = NULL);
 
diff --git a/src/EntityEmbedDisplay/FieldFormatterEntityEmbedDisplayBase.php b/src/EntityEmbedDisplay/FieldFormatterEntityEmbedDisplayBase.php
index 79456c2..f681c56 100644
--- a/src/EntityEmbedDisplay/FieldFormatterEntityEmbedDisplayBase.php
+++ b/src/EntityEmbedDisplay/FieldFormatterEntityEmbedDisplayBase.php
@@ -7,6 +7,7 @@
 
 namespace Drupal\entity_embed\EntityEmbedDisplay;
 
+use Drupal\Core\Access\AccessResult;
 use Drupal\Core\Entity\EntityManagerInterface;
 use Drupal\Core\Field\BaseFieldDefinition;
 use Drupal\Core\Field\FormatterPluginManager;
@@ -112,12 +113,12 @@ abstract class FieldFormatterEntityEmbedDisplayBase extends EntityEmbedDisplayBa
    * {@inheritdoc}
    */
   public function access(AccountInterface $account = NULL) {
-    if (!parent::access($account)) {
-      return FALSE;
-    }
+    return parent::access($account)->andIf($this->isApplicableFieldFormatter());
+  }
 
+  protected function isApplicableFieldFormatter() {
     $definition = $this->formatterPluginManager->getDefinition($this->getDerivativeId());
-    return $definition['class']::isApplicable($this->getFieldDefinition());
+    return AccessResult::allowedIf($definition['class']::isApplicable($this->getFieldDefinition()));
   }
 
   /**
diff --git a/src/Plugin/entity_embed/EntityEmbedDisplay/ImageFieldFormatter.php b/src/Plugin/entity_embed/EntityEmbedDisplay/ImageFieldFormatter.php
index b75fd14..e66c5fc 100644
--- a/src/Plugin/entity_embed/EntityEmbedDisplay/ImageFieldFormatter.php
+++ b/src/Plugin/entity_embed/EntityEmbedDisplay/ImageFieldFormatter.php
@@ -7,6 +7,7 @@
 
 namespace Drupal\entity_embed\Plugin\entity_embed\EntityEmbedDisplay;
 
+use Drupal\Core\Access\AccessResult;
 use Drupal\Core\Entity\EntityManagerInterface;
 use Drupal\Core\Field\FormatterPluginManager;
 use Drupal\Core\Form\FormStateInterface;
@@ -85,15 +86,21 @@ class ImageFieldFormatter extends FileFieldFormatter {
    * {@inheritdoc}
    */
   public function access(AccountInterface $account = NULL) {
-    if (!parent::access($account)) {
-      return FALSE;
-    }
+    return parent::access($account)->andIf($this->isValidImage());
+  }
+
+  protected function isValidImage() {
+    $access = AccessResult::allowed();
 
+    // @todo needs cacheability metadata for getEntityFromContext.
+    // @see \Drupal\entity_embed\EntityEmbedDisplay\EntityEmbedDisplayBase::getEntityFromContext()
     if ($entity = $this->getEntityFromContext()) {
-      return $this->imageFactory->get($entity->getFileUri())->isValid();
+      $access = AccessResult::allowedIf($this->imageFactory->get($entity->getFileUri())->isValid())
+        // See the above @todo, this is the best we can do for now.
+        ->addCacheableDependency($entity);
     }
 
-    return TRUE;
+    return $access;
   }
 
   /**