This article sets the stage for a debate, played out in two subsequent articles in this issue by Glenberg and by Mahon, regarding the role of embodied conceptual representations in cognitive operations such as language understanding and object identification. On an embodied view of cognition, championed by Glenberg, conceptual knowledge and thought are necessarily grounded in sensorimotor representations. The contrary position, advocated by Mahon, is that symbolic thought is the foundation for cognition and is independent of such representations, although it may coincidentally evoke them. I review a few of the many available demonstrations showing that cognition is influenced by sensorimotor representations. Then, taking Mahon's perspective, I illustrate how examples from various classes of these demonstrations can be explained by mechanisms other than embodiment of conceptual representations. I close with an example of what can be taken as evidence for the representation of a behavioural goal that is abstract in the sense that it is not coded directly as an embodied action.