There is increasingly much agreement in the cognitive sciences that human cognition is embodied – to some significant extent. However, there is much less agreement regarding in what sense(s) cognition is embodied. In particular, there is much agreement that sensorimotor interaction with the environment is fundamental to cognition. From a historical perspective, this emphasis on the sensorimotor body is at least partly due to the crucial role that the conceptual shift in artificial intelligence (AI) research – from computational to robotic models – has played in the overall development of embodied cognitive science. Most embodied AI research, however, in particular work on symbol grounding and related approaches, reduces the body to a mere sensorimotor interface for internal processes that are still just as computational as they were 30–40 years ago. In Harnad's terms, this type of AI has only gone from a computational to a robotic functionalism. In theory, this could be limited to AI research as such, but in practice the view of the physical body as the computational mind's sensorimotor interface to the world still pervades much of cognitive science and philosophy of mind. The argument presented here is that there are good reasons to say that at least today's robots are in fact not embodied – in any sense that would allow for anything even close to human embodied cognition and intentionality – and that this has implications for social interactions between humans and robots.