The face morphing attack enables the illegitimate sharing of photo-ID documents intended for identity verification. Multiple users may use the same passport, driver license or health insurance card without being condemned. This paper summarizes recent advances in protecting the photo-ID-based verification from the morphing attack. We explain the attack along with the standard approach of creating morphed face images. We identify research gaps and open challenges by summarizing studies assessing the potential of the morphing attack as well as studies concerned with generating databases of morphed face images and examining the performance of morphing detectors. We discuss new performance metrics looking for conformity with the standard on presentation attack detection. Based on the current advances, we recommend technical and organizational security mechanisms to mitigate or even prevent the morphing attack.