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In this chapter we give and up to date overview of papers that combine research in image compression and face recognition. In almost every imaginable real life face recognition scenario, image compression seems unavoidable, and standard JPEG and JPEG2000 compression schemes seem to be the logical choice. As a prerequisite to implementing compression in face recognition systems, two important questions have to be answered. The first one is how does image degradation that naturally comes from a lossy compression scheme affect recognition accuracy. The second one is can face recognition be performed directly in compressed domain, without fully decompressing the images, and how that kind of approach affect the recognition accuracy. This paper will present conclusions from papers published up to now that tried to answer those questions. We shall show that most researches agree that compression does not significantly deteriorate recognition accuracy in both cases. Nevertheless, as this survey will show, research on this subject is still at its pioneering stage and a lot of work is still to be done (especially in the compressed domain recognition) to reach the real life implementation stage.