Music frequently elicits intense emotional responses, a phenomenon that has been scrutinized from multiple disciplines that span the sciences and arts. While most people enjoy music and find it rewarding, there is substantial individual variability in the experience and degree of music‐induced reward. Here, we review current work on the neural substrates of hedonic responses to music. In particular, we focus the present review on specific musical anhedonia, a selective lack of pleasure from music. Based on evidence from neuroimaging, neuropsychology, and brain stimulation studies, we derive a neuroanatomical model of the experience of pleasure during music listening. Our model posits that hedonic responses to music are the result of connectivity between structures involved in auditory perception as a predictive process, and those involved in the brain's dopaminergic reward system. We conclude with open questions and implications of this model for future research on why humans appreciate music.