Neonatal imitation has rich implications for neuroscience, developmental psychology, and social cognition, but there is little consensus about this phenomenon. The primary empirical question, whether or not neonatal imitation exists, is not settled. Is it possible to give a balanced evaluation of the theories and methodologies at stake so as to facilitate real progress with respect to the primary empirical question? In this paper, we address this question. We present the operational definition of differential imitation and discuss why it is important to keep it in mind. The operational definition indicates that neonatal imitation may not look like prototypical imitation and sets non-obvious requirements on what can count as evidence for imitation. We also examine the principal explanations for the extant findings and argue that two theories, the arousal hypothesis and the Association by Similarity Theory, which interprets neonatal imitation as differential induction of spontaneous behavior through similarity, offer better explanations than the others. With respect to methodology, we investigate what experimental design can best provide evidence for imitation, focusing on how differential induction may be maximized and detected. Finally, we discuss the significance of neonatal imitation for the field of social cognition. Specifically, we propose links with theories of social interaction and direct social perception. Overall, our goals are to help clarify the complex theoretical issues at stake and suggest fruitful guidelines for empirical research.