Where in drupal 7 you would typically use something like drupal_get_path_alias(), this is different in drupal 8. Below the code to get the curren alias of your route:
Sometimes it is needed for a user to be redirected after registration. The user is not logged in yet, and has to go to a landing page with more instructions on verifying his e-mail.
foreach (\Drupal::routeMatch()->getParameters() as $entity) {
if ($entity instanceof \Drupal\Core\Entity\EntityInterface) {
// here $entity is your object
}
}