We present a review on perception and cognition models designed for or applicable to music. An emphasis is put on computational implementations. We include findings from different disciplines: neuroscience, psychology, cognitive science, artificial intelligence, and musicology. The article summarizes the methodology that these disciplines use to approach the phenomena of music understanding, the localization of musical processes in the brain, and the flow of cognitive operations involved in turning physical signals into musical symbols, going from the transducers to the memory systems of the brain. We discuss formal models developed to emulate, explain and predict phenomena involved in early auditory processing, pitch processing, grouping, ...