Emotion-related areas of the brain, such as the medial frontal cortices, amygdala, and striatum, are activated during listening to sad or happy music as well as during listening to pleasurable music. Indeed, in music, like in other arts, sad and happy emotions might co-exist and be distinct from emotions of pleasure or enjoyment. Here we aimed at discerning the neural correlates of sadness or happiness in music as opposed those related to musical enjoyment. We further investigated whether musical expertise modulates the neural activity during affective listening of music. To these aims, 13 musicians and 16 non-musicians brought to the lab their most liked and disliked musical pieces with a happy and sad connotation. Based on a listening test, we selected the most representative 18 sec excerpts of the emotions of interest for each individual participant. Functional magnetic resonance imaging (fMRI) recordings were obtained while subjects listened to and rated the excerpts. The cortico-thalamo-striatal reward circuit and motor areas were more active during liked than disliked music, whereas only the auditory cortex and the right amygdala were more active for disliked over liked music. These results discern the brain structures responsible for the perception of sad and happy emotions in music from those related to musical enjoyment. We also obtained novel evidence for functional differences in the limbic system associated with musical expertise, by showing enhanced liking-related activity in fronto-insular and cingulate areas in musicians.