There has recently been a growing interest to investigate rhythm cognition in nonhuman animals as a way of tracking the evolutionary origins of human musicality - i.e., the ability to perceive, enjoy and produce music. During the last two decades, there has been an explosion of theoretical proposals aimed at explaining why and how humans have evolved into musical beings, and the empirical comparative research has also gained momentum. In this paper, we focus on the rhythmic component of musicality, and review functional and mechanistic theoretical proposals on abilities regarded as prerequisites for perceiving and producing rhythmic structures similar to those encountered in music. For each theoretical proposal we also review supporting and contradictory empirical findings. To acknowledge that the evolutionary study of musicality requires an interdisciplinary approach, our review strives to cover perspectives and findings from as many disciplines as possible. We conclude with a research agenda that highlights relevant, yet thus far neglected topics in the comparative and evolutionary study of rhythm cognition. Specifically, we call for a widened research focus that will include additional rhythmic abilities besides entrainment, additional channels of perception and production besides the auditory and vocal ones, and a systematic focus on the functional contexts in which rhythmic signals spontaneously occur. With this expanded focus, and drawing from systematic observation and experimentation anchored in multiple disciplines, animal research is bound to generate many important insights into the adaptive pressures that forged the component abilities of human rhythm cognition and their (socio-)cognitive and (neuro-)biological underpinnings.