Radiofrequency heating in toroidal geometry is described. Starting from a general theory, expressions for the dielectric response and the radiofrequency diffusion operator are obtained. The computationally most efficient simplified expressions bear a close resemblance to the results of uniform plasma theory, but differ from them in their interpretation. In cases where the simplified expressions do not describe the physics faithfully, more general but computationally slower ones are available. Rigorously accounting for the geometry and the wave field yields fine structure that is commonly overlooked. Aside from causing the well-known k∥-upshift or downshift impacting on the Doppler shift, the non-zero poloidal magnetic field modifies the orbital topology and forces one to account for the poloidal inhomogeneity of the static magnetic field. The expressions obtained restore intuition on how an electric field interacts with a charged particle, but, in so doing, cast doubt on the degree of realism of predictions of simplified models that do not account for the constructive or destructive interference phenomena introduced by the orbital topology non-uniformity. The expressions represent a numerical challenge, but show the necessity for the detailed description: the ‘coarse-graining’ underlying simplified models yields a result that has the right order of magnitude for interference related to crosstalk between resonances or multiple encounters with a given resonance, but may be an order of magnitude wrong for predictions on the combined effect of a poloidal mode spectrum. A Fokker–Planck code BATCH (Bounce-Averaged Tool for Cyclotron Heating), relying on the expressions obtained, is presented and some results are discussed.