Humans possess an ability to perceive and synchronize movements to the beat in music (‘beat perception and synchronization’), and recent neuroscientific data have offered new insights into this beat-finding capacity at multiple neural levels. Here, we review and compare behavioural and neural data on temporal and sequential processing during beat perception and entrainment tasks in macaques (including direct neural recording and local field potential (LFP)) and humans (including fMRI, EEG and MEG). These abilities rest upon a distributed set of circuits that include the motor cortico-basal-ganglia–thalamo-cortical (mCBGT) circuit, where the supplementary motor cortex (SMA) and the putamen are critical cortical and subcortical nodes, respectively. In addition, a cortical loop between motor and auditory areas, connected through delta and beta oscillatory activity, is deeply involved in these behaviours, with motor regions providing the predictive timing needed for the perception of, and entrainment to, musical rhythms. The neural discharge rate and the LFP oscillatory activity in the gamma- and beta-bands in the putamen and SMA of monkeys are tuned to the duration of intervals produced during a beat synchronization–continuation task (SCT). Hence, the tempo during beat synchronization is represented by different interval-tuned cells that are activated depending on the produced interval. In addition, cells in these areas are tuned to the serial-order elements of the SCT. Thus, the underpinnings of beat synchronization are intrinsically linked to the dynamics of cell populations tuned for duration and serial order throughout the mCBGT. We suggest that a cross-species comparison of behaviours and the neural circuits supporting them sets the stage for a new generation of neurally grounded computational models for beat perception and synchronization.