Advances in robotics and multisensory displays allow extending telepresence ambitions beyond only "the feeling of being present at a remote location". In this paper, we discuss what may lie beyond telepresence and how we can transport both the functional and social self of a user. We introduce the embodiment illusion and its potential contribution to task performance and list important cues to evoke this illusion, including synchronicity in multisensory information, a firstperson visual perspective, and a human-like visual appearance and anatomy of the telepresence robot. We also introduce the concept of social presence and the important bidirectional social cues it needs, including eye contact, facial expression, posture, gestures, and social touch. For all these multisensory and social cues, we explain how they can be implemented in a telepresence system and describe our solution consisting of a closed control pod and a humanoid telepresence robot.