The fundamental theory of plasma heating by the fast magnetosonic wave in toroidal plasma configurations is reviewed and extended. The particular wave damping processes considered include cyclotron damping at the fundamental ion cyclotron frequency and its harmonics, and electron Landau damping and transist time magnetic pumping (TTMP). The latter processes heat electrons and may also be exploited to drive toroidal plasma currents. The wave absorption and damping decrements are obtained by using Stix’s approach, namely by computing the dissipated power, R e(J̄⋅Ē) in terms of the hot plasma dielectric constant (where J̄ is the wave induced current). This approach is compared with power absorption calculations from quasi‐linear theory, and exact agreement is found for a Maxwellian distribution of particles. Wave absorption in the presence of a small group of energetic particles is also examined for all three types of damping processes. The limitations of theory owing to mode conversion phenomena are indicated. Finally, a brief discussion of recent experimental results is given, verifying the reality of Landau damping of magnetosonic waves by electrons.