Despite more than 100 years of research, there is no agreement among experts as to whether or not primates can imitate. Part of the problem is that there is little agreement as to what constitutes an example of “imitation.” Nevertheless, recent research provides compelling evidence for both continuities and discontinuities in the psychological faculty that mediates imitation performance. A number of studies have shown that monkeys and apes are capable of copying familiar responses, but it is questionable whether they can also copy novel responses, particularly those involving novel tool-related actions. These results have been interpreted to mean that primates cannot engage in “imitation learning” or novel imitation. Yet there is some evidence showing that monkeys can imitate novel “cognitive” rules (i.e., ordinal rules of the form Apple-Boy-Cat) independently of copying specific motor responses. Rather than suggesting that monkeys and other primates are poor imitators, these results suggest that primates can learn novel cognitive rules but not novel motor rules, possibly because such skills require derived neural specializations in the Parietal Lobe linking social and physical cognitive skills. If true, such evidence represents an important discontinuity between the imitation skills of human and non-human primates with significant implications for human cognitive evolution.