Sensorimotor synchronization (SMS), the rhythmic coordination of perception and action, occurs in many contexts, but most conspicuously in music performance and dance. In the laboratory, it is most often studied in the form of finger tapping to a sequence of auditory stimuli. This review summarizes theories and empirical findings obtained with the tapping task. Its eight sections deal with the role of intention, rate limits, the negative mean asynchrony, variability, models of error correction, perturbation studies, neural correlates of SMS, and SMS in musical contexts. The central theoretical issue is considered to be how best to characterize the perceptual information and the internal processes that enable people to achieve and maintain SMS. Recent research suggests that SMS is controlled jointly by two error correction processes (phase correction and period correction) that differ in their degrees of cognitive control and may be associated with different brain circuits. They exemplify the general distinction between subconscious mechanisms of action regulation and conscious processes involved in perceptual judgment and action planning.