Listening to music is above all a human experience, which becomes an aesthetic experience when an individual immerses himself/herself in the music, dedicating attention to perceptual-cognitive-affective interpretation and evaluation. The study of these processes where the individual perceives, understands, enjoys and evaluates a set of auditory stimuli has mainly been focused on the effect of music on specific brain structures, as measured with neurophysiology and neuroimaging techniques. The very recent application of network science algorithms to brain research allows an insight into the functional connectivity between brain regions. These studies in network neuroscience have identified distinct circuits that function during goal-directed tasks and resting states. We review recent neuroimaging findings which indicate that music listening is traceable in terms of network connectivity and activations of target regions in the brain, in particular between the auditory cortex, the reward brain system and brain regions active during mind wandering.