Drupal 8 block with custom cache context and tags

MyCustomBlock.php

<?php

class MyCustomBlock extends BlockBase {
  public function build() {
    return array(
      '#markup' => $this->t('My custom block content'),
      '#cache' => array(
        'contexts' => ['url.path'], // https://www.drupal.org/developing/api/8/cache/contexts
        'tags' => ['node:1', 'node:2'] // https://www.drupal.org/developing/api/8/cache/tags
      ),
    );
  }
}

Note that ENTITYNAME_list such as node_list are appropriate tag names as well, which invalidate whenever any entity of that type is added/edited/deleted.

Instead of hardcoding ENTITYTYPE_list, you can find it by calling the function that provides them:

\Drupal::entityManager()->getDefinition('ENTITYTYPE')->getListCacheTags(),

In most cases, that will just return "ENTITYTYPE_list" but not necessarily always, if a given entity class has overridden its $this->list_cache_tags property.

Here is an example from a custom block in Drupal 8:
use Drupal\Core\Cache\Cache;

return [
'#theme' => 'user_profile_template',
'#user_data' => $user_data,
'#cache' => [
'tags' => ['languages', 'timezone'],
'contexts' => ['node:5', 'user:3'],
'max-age' => Cache::PERMANENT,
],
];

We can also define our own cache tag:
Request a cache object through \Drupal::cache().
Define a Cache ID (cid) value for your data. A cid is a string, which must contain enough information to uniquely identify the data.
Call the get() method to attempt a cache read, to see if the cache already contains your data.
If your data is not already in the cache, compute it and add it to the cache using the set() method.
$nid = 9;
$cid = 'my_module:' . $nid;

// Check if the cache already contain data.
if ($item = \Drupal::cache()->get($cid)) {
return $item->data;
}

// The data to be cached.
$node = Node::load($nid);
$data = [
'title' => sprintf('## %s', $node->get('title')->getValue()),
//...
];

// Set the cache for 'my_module:' . $nid cache tag until $node changes.
\Drupal::cache()->set($cid, $data, Cache::PERMANENT, $node->getCacheTags());

Check out How does entity cache work in Drupal 8