In this article, we review recent advances in research on rhythm and musical beat perception, focusing on the role of predictive processes in auditory motor interactions. We suggest that experimental evidence of the motor system's role in beat perception, including in passive listening, may be explained by the generation and maintenance of internal predictive models, concordant with the Active Inference framework of sensory processing. We highlight two complementary hypotheses for the neural underpinnings of rhythm perception: The Action Simulation for Auditory Prediction hypothesis (Patel and Iversen, 2014) and the Gradual Audiomotor Evolution hypothesis (Merchant and Honing, 2014) and review recent experimental progress supporting each of these hypotheses. While initial formulations of ASAP and GAE explain different aspects of beat-based timing-the involvement of motor structures in the absence of movement, and physical entrainment to an auditory beat respectively-we suggest that work under both hypotheses provide converging evidence toward understanding the predictive role of the motor system in the perception of rhythm, and the specific neural mechanisms involved. We discuss future experimental work necessary to further evaluate the causal neural mechanisms underlying beat and rhythm perception.