Cavity magnonics deals with the interaction of magnons — elementary excitations in magnetic materials — and confined electromagnetic fields. We introduce the basic physics and review the experimental and theoretical progress of this young field that is gearing up for integration in future quantum technologies. Much of its appeal is derived from the strong magnon–photon coupling and the easily-reached nonlinear regime in microwave cavities. The interaction of magnons with light as detected by Brillouin light scattering is enhanced in magnetic optical resonators, which can be employed to cool and heat magnons. The microwave cavity photon-mediated coupling of a magnon mode to a superconducting qubit enables measurements in the single magnon limit.