The vulnerability of Face Recognition System (FRS) to various kind of attacks (both direct and in-direct attacks) and face morphing attacks has received a great interest from the biometric community. The goal of a morphing attack is to subvert the FRS at Automatic Border Control (ABC) gates by presenting the Electronic Machine Readable Travel Document (eMRTD) or e-passport that is obtained based on the morphed face image. Since the application process for the e-passport in the majority countries requires a passport photo to be presented by the applicant, a malicious actor and the accomplice can generate the morphed face image and to obtain the e-passport. An e-passport with a morphed face images can be used by both the malicious actor and the accomplice to cross the border as the morphed face image can be verified against both of them. This can result in a significant threat as a malicious actor can cross the border without revealing the track of his/her criminal background while the details of accomplice are recorded in the log of the access control system. This survey aims to present a systematic overview of the progress made in the area of face morphing in terms of both morph generation and morph detection. In this paper, we describe and illustrate various aspects of face morphing attacks, including different techniques for generating morphed face images but also the state-of-the-art regarding Morph Attack Detection (MAD) algorithms based on a stringent taxonomy and finally the availability of public databases, which allow to benchmark new MAD algorithms in a reproducible manner. The outcomes of competitions/benchmarking, vulnerability assessments and performance evaluation metrics are also provided in a comprehensive manner. Furthermore, we discuss the open challenges and potential future works that need to be addressed in this evolving field of biometrics.