Filter input text with Drupal Text Formats

Like Drupal 7, you can use check_markup();

CAUTION : This must only use on a rendered HTML page

$text_out = check_markup($text, $format_id = NULL, $langcode = '', $filter_types_to_skip = array())
$text_out => \Drupal\Component\Render\MarkupInterface The filtered text.

Example:
$text = "<b>Your</b> <h1>Html</h1> <u>Text</u>"
$text_out = check_markup($text, 'basic_html'); //Return text using Basic Html Filter settings
$text_out = check_markup($text); //Return text using default settings
//dpm($text_out."");