Music exists in all cultures and appears to elicit intense emotions and pleasure in the vast majority of people. Recent scientific advances have linked the pleasure of music listening to biological mechanisms associated with rewarding or reinforcing stimuli, including the activation of the brain’s reward system. Specifically, we and others have shown that the neurotransmitter dopamine is central to this phenomenon, and that it engages one subregion of the reward system in anticipation of pleasurable musical events and another during its realization. This dissociation implies that musical pleasure operates via some predictive mechanism that creates expectations, which the music then either fulfills or not. Accordingly, a growing body of evidence highlights the prevalence of prediction-based neural processing and its importance for learning about and adapting to one’s environment. Drawing on these findings and on related research into the optimization of learning, we propose that musical structures recruit neural systems of reward and emotion by evoking sufficiently uncertain expectations to build anticipation, and sufficiently surprising events to foster learning, reward, and pleasure. We explore the role that musical experience and culture play in engendering expectations, and offer suggestions for future research into the neuroscience of musical aesthetics and reward.