Questions about whether music is meaningful, or has meaning, what kinds of meaning it has, and how it has those meanings, have preoccupied writers on music for two and a half millennia. Plato and Aristotle wondered and worried about the effects of music on people— and in some sense were therefore concerned with what music meant to people. Since then a huge volume and diversity of thinking and writing has grappled with this most fundamental and still elusive question about music, from perspectives that range from neuroscience through psychology, linguistics, semiotics, sociology and anthropology, to the very large volume of philosophical writing. Given this very diverse literature, and in the context of the overall focus of this Companion, the aim of this chapter is to consider those approaches that are broadly psychological, or which in one way or another are connected with psychological methods or considerations. Since even this narrowing of the terrain leaves a potentially huge array of fascinating ideas, what follows will be selectively thematic rather than in any sense encyclopedic.