Music and dance require coordination in time. This can take many different forms, including simple synchronization, and is often referred to as entrainment. Although entrainment abilities are present in several non-human species to varying degrees, humans can entrain to complex signals and adapt almost instantly and effortlessly to both small and large temporal changes, while at the same time performing complex, coordinated movement patterns. This chapter reviews significant features of human entrainment that realistic models of entrainment should be able to account for. Different strands of data suggest that a viable model consists of a neural representation of a hierarchical time structure superimposed on a regular beat, as reflected in the metrical structure of music. This temporal grid provides an optimized representation of both short and long time intervals with sufficient precision for functional synchrony, as well as a framework for very complex temporal patterns. The beat is an iterative temporal prediction based on recent events, adaptive to both gradual and sudden tempo changes.