Theme Modifications

You can use the native WordPress function do_shortcode to execute a shortcode in your plugin or theme.

If you use the function tag_groups_cloud with the last parameter set to true, it will return an array instead of the HTML.

if (function_exists('tag_groups_cloud')) $output = tag_groups_cloud(array('amount' => 20), true);

more info about the parameters

You can request data through custom endpoints of the REST API. (Currently it is only possible to read data.)