The quantum monad on relational structures was introduced by Abramsky, Barbosa, De Silva and Zapata (2017). It encapsulates the use of quantum resources to provide advantage in classical information processing tasks such as graph homomorphisms, constraint satisfactions problems, and games. The (graded) monad structure is widely used in modern functional programming languages. We introduce the quantum monad and its relationship to quantum homomorphisms, non-local games, and state-independent contextuality. We also discuss recent work by Karamlou relating the quantum monad to game comonads, which arise in finite model theory and descriptive complexity.