Face Anti-Spoofing (FAS), also referred to as Face Liveness, has emerged as a rapidly evolving field of research in Computer Vision. Closely tied to Face Recognition, its primary objective is to authenticate an identity by verifying its authenticity. However, safeguarding against diverse types of spoof attacks poses significant challenges due to the vast range of spoofing methods, capture devices, and environments. To mitigate this issue, researchers frequently employ Domain Generalization and Domain Adaptation approaches. This paper presents a comprehensive review of the latest deep learning-based FAS techniques that have achieved state-of-the-art results using the leave-one-domain-out protocol and the OCIM evaluation method, a common benchmark in both Domain Generalization and Domain Adaptation FAS. Finally, we conclude this survey by exploring potential new research directions in FAS. © 2013 IEEE.