Human interaction often requires simultaneous precision and flexibility in the coordination of rhythmic behaviour between individuals engaged in joint activity, for example, playing a musical duet or dancing with a partner. This review article addresses the psychological processes and brain mechanisms that enable such rhythmic interpersonal coordination. First, an overview is given of research on the cognitive-motor processes that enable individuals to represent joint action goals and to anticipate, attend and adapt to other's actions in real time. Second, the neurophysiological mechanisms that underpin rhythmic interpersonal coordination are sought in studies of sensorimotor and cognitive processes that play a role in the representation and integration of self- and other-related actions within and between individuals' brains. Finally, relationships between social–psychological factors and rhythmic interpersonal coordination are considered from two perspectives, one concerning how social-cognitive tendencies (e.g. empathy) affect coordination, and the other concerning how coordination affects interpersonal affiliation, trust and prosocial behaviour. Our review highlights musical ensemble performance as an ecologically valid yet readily controlled domain for investigating rhythm in joint action.