Musicians have long framed their creative activity within constraints, whether imposed externally or consciously chosen. As noted by Leonard Meyer, any style can be viewed as an ensemble of constraints, requiring the features of the artwork to conform with accepted norms. Such received stylistic constraints may be complemented by additional, voluntary limitations: for example, using only a limited palette of pitches or sounds, setting rules to govern repetition or transformation, controlling the formal layout and proportions of the work, or limiting the variety of operations involved in its creation. This chapter proposes a fourfold classification of the limits most often encountered in music creation into material (absolute and relative), formal, style/genre, and process constraints. The role of constraints as a spur and guide to musical creativity is explored in the domains of composition, improvisation, performance, and even listening, with examples drawn from contemporary composers including György Ligeti, George Aperghis, and James Tenney. Such musical constraints are comparable to self-imposed limitations in other art forms, from film (the Dogme 95 Manifesto) and visual art (Robert Morris’s Blind Time Drawings) to the writings of authors associated with the Oulipo (Ouvroir de littérature potentielle) such as Georges Perec and Raymond Queneau.