Music is a pervasive phenomenon in human culture, and musical rhythm is virtually present in all musical traditions. Research on the evolution and cognitive underpinnings of rhythm can benefit from a number of approaches. We outline key concepts and definitions, allowing fine-grained analysis of rhythmic cognition in experimental studies. We advocate comparative animal research as a useful approach to answer questions about human music cognition and review experimental evidence from different species. Finally, we suggest future directions for research on the cognitive basis of rhythm. Apart from research in semi-natural setups, possibly allowed by "drum set for chimpanzees" prototypes presented here for the first time, mathematical modeling and systematic use of circular statistics may allow promising advances.