Music research has increasingly focused on neural responses to naturalistic stimuli. The neural correlates of music-induced peak moments of pleasure (e.g., chills) have been well-studied; data on other types of aesthetic responses, such as judgments of beauty, goodness, or liking are sparse. Among these, liking is of particular interest given its complex nature and its ubiquity in everyday and musical experiences. In this functional magnetic resonance imaging (fMRI) study, 26 participants listened to musical excerpts while continuously rating how much they liked the music. In addition, subjects provided an overall liking judgment at the end of each musical piece. Participants\' musical preferences manifested remarkably early and were sustained over time, with the value of the continuous rating at the end of each piece showing the strongest correlation with the overall ratings. At the neural level, highly liked and disliked musical pieces activated a shared neural network previously associated with the processing of both positive and negative emotional stimuli. This network encompassed the anterior cingulate cortex, limbic system, basal ganglia, and precuneus. These activations reflected individual differences, such that participants with greater trait-level responsiveness to artistic stimuli showed stronger engagement of this network while listening to music. Finally, the default-mode network was associated with the slope of the continuous ratings, suggesting that the faster participants liked a musical excerpt, the more disengaged this network became. In linking behavior and brain function to better characterize the way humans make aesthetic judgments of music the data support a model in which preferences and aesthetic choices are modulated by brain circuits associated with emotion and reward.