The limited capacity to recognise faces under occlusions is a long-standing problem that presents a unique challenge for face recognition systems and even humans. The problem regarding occlusion is less covered by research when compared to other challenges such as pose variation, different expressions, etc. Nevertheless, occluded face recognition is imperative to exploit the full potential of face recognition for real-world applications. In this article, the scope to occluded face recognition is restricted and a systematic categorisation that new as well as classic methods fit into is presented. First, the authors explore the kind of the occlusion problem and the type of inherent difficulties that can arise. As a part of this review, face detection under occlusion, a preliminary step in face recognition. Second the authors analyse how the existing face recognition methods cope with the occlusion problem and classify them into three categories, which are given as: 1) occlusion robust feature extraction approaches, 2) occlusion aware face recognition approaches, and 3) occlusion recovery based face recognition approaches. Furthermore, the motivations, innovations, pros and cons, and the performance of representative approaches for comparison are analyzed. Finally, future challenges and method trends of occluded face recognition are thoroughly discussed.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.