The embodied cognition approach to the study of the mind proposes that higher order mental processes such as concept formation and language are essentially based on perceptual and motor processes. Contrary to the classical approach in cognitive science, in which concepts are viewed as amodal, arbitrary symbols, embodied semantics argues that concepts must be "grounded" in sensorimotor experiences in order to have meaning. In line with this view, neuroimaging studies have shown a roughly somatotopic pattern of activation along cortical motor areas (broadly construed) for the observation of actions involving different body parts, as well as for action-related language comprehension. These findings have been interpreted in terms of a mirror-neuron system, which automatically matches observed and executed actions. However, the somatotopic pattern of activation found in these studies is very coarse, with significant overlap between body parts, and sometimes with multiple representations for the same body part. Furthermore, the localization of the respective activations varies considerably across studies. Based on recent work on the motor cortex in monkeys, we suggest that these discrepancies result from the organization of the primate motor cortex (again, broadly construed), which probably includes maps of the coordinated actions making up the individual's motor repertoire, rather than a single, continuous map of the body. We review neurophysiological and neuroimaging data supporting this hypothesis and discuss ways in which this framework can be used to further test the links between neural mirroring and linguistic processing. (Contains 1 table and 1 figure.)