This chapter provides a structured overview of studies accounting for the aesthetic responses to music. Bottom-up accounts linking preference with determined stimulus features are distinguished from other cognitivist, emotivist, or contextual accounts putting more weight on nonappearance properties related to the individual life experience. Additionally, models of the musical aesthetic experience that emphasize psychological processes are illustrated as distinct from models that account also for the neural mechanisms involved. While most findings concentrate on the aesthetic response of pleasure or preference, fresh efforts are projected toward understanding other aesthetically tinged dimensions such as evaluative judgments and attitudes. Naturalistic approaches are promising toward understanding from the daily drive to musical activities to the life-changing peak experiences of music.