Cognitive neuroscientists have contributed to the understanding of imitation according to their expertise. Neuropsychologists first established over a century ago that lesions to the left hemisphere of right-handed individuals lead to a dramatic reduction of their ability to imitate gestures. In contrast, after frontal lobe damage, patients may experience severe difficulties in inhibiting their imitative tendency. These findings suggested that our tendency to imitate is mostly sustained by the left hemisphere and that we normally manage successfully to keep it under control. Neuropsychologists went on investigating other aspects of gesture imitation. These include the existence of putative mechanisms involved in imitating different types of gestures (e.g. meaningful and meaningless or transitive and intransitive), the strategic control over these mechanisms and whether there are differences in imitation depending on the action goal or the body part used. Based on neuropsychological findings, some cognitive models of gesture imitation have been forwarded, the most influential of which will be reviewed here. In particular, reference will be made to the dual route model and to accounts that associate the imitative deficit to putative degraded body representations.