The last ten years have seen an increasing interest, within cognitive science, in issues concerning the physical body, the local environment, and the complex interplay between neural systems and the wider world in which they function. Yet many unanswered questions remain, and the shape of a genuinely physically embodied, environmentally embedded science of the mind is still unclear. In this article I will raise a number of critical questions concerning the nature and scope of this approach, drawing a distinction between two kinds of appeal to embodiment: (1) 'Simple' cases, in which bodily and environmental properties merely constrain accounts that retain the focus on inner organization and processing; and (2) More radical appeals, in which attention to bodily and environmental features is meant to transform both the subject matter and the theoretical framework of cognitive science.