Virtual self-avatars have been increasingly used in Augmented Reality (AR) where one can see virtual content embedded into physical space. However, little is known about the perception of self-avatars in such a context. The possibility that their embodiment could be achieved in a similar way as in Virtual Reality opens the door to numerous applications in education, communication, entertainment, or the medical field. This article aims to review the literature covering the embodiment of virtual self-avatars in AR. Our goal is (i) to guide readers through the different options and challenges linked to the implementation of AR embodiment systems, (ii) to provide a better understanding of AR embodiment perception by classifying the existing knowledge, and (iii) to offer insight on future research topics and trends for AR and avatar research. To do so, we introduce a taxonomy of virtual embodiment experiences by defining a "body avatarization" continuum. The presented knowledge suggests that the sense of embodiment evolves in the same way in AR as in other settings, but this possibility has yet to be fully investigated. We suggest that, whilst it is yet to be well understood, the embodiment of avatars has a promising future in AR and conclude by discussing possible directions for research.