Every human culture has some form of music with a beat: a perceived periodic pulse that structures the perception of musical rhythm and which serves as a framework for synchronized movement to music. What are the neural mechanisms of musical beat perception, and how did they evolve? One view, which dates back to Darwin and implicitly informs some current models of beat perception, is that the relevant neural mechanisms are relatively general and are widespread among animal species. On the basis of recent neural and cross-species data on musical beat processing, this paper argues for a different view. Here we argue that beat perception is a complex brain function involving temporally-precise communication between auditory regions and motor planning regions of the cortex (even in the absence of overt movement). More specifically, we propose that simulation of periodic movement in motor planning regions provides a neural signal that helps the auditory system predict the timing of upcoming beats. This “action simulation for auditory prediction” (ASAP) hypothesis leads to testable predictions. We further suggest that ASAP relies on dorsal auditory pathway connections between auditory regions and motor planning regions via the parietal cortex, and suggest that these connections may be stronger in humans than in non-human primates due to the evolution of vocal learning in our lineage. This suggestion motivates cross-species research to determine which species are capable of human-like beat perception, i.e., beat perception that involves accurate temporal prediction of beat times across a fairly broad range of tempi.