Although an increasing number of cognitive scientists are convinced that cognition is embodied, there still is relatively little agreement on what exactly that means. Notions of what it actually means for a cognizer to be embodied range from simplistic ones such as ‘being physical’ or ‘interacting with an environment’ to more demanding ones that consider a particular morphology or a living body prerequisites for embodied cognition. Based on experimental evidence from a range of disciplines, we argue that one of the keys to understanding the embodiment of cognition is the sharing of neural mechanisms between sensorimotor processes and higher-level cognitive processes. The latter are argued to be embodied in the sense that they make use of (partial) simulations or emulations of sensorimotor processes through the re-activation of neural circuitry also active in bodily perception and action.