The review specializes to the modelling of plasmas in a particular type of fusion experiment, namely the tokamak. Simulation is taken to imply the use of a model which involves variation in at least two coordinate directions and is nonlinear, the nonlinearity invariably being of the advective type. Developments in the period 1976-1992 are covered under five main headings, with particle methods constituting the first. The remaining four concern the solution via mesh-based methods of (1) the Fokker-Planck equation, (2) drift-wave problems, (3) edge models and (4) time-dependent magnetohydrodynamic problems. Care is taken to outline the capabilities of the currently available software. Progress in the. Design of numerical algorithms for the mesh-based simulations is found to have been incremental rather than revolutionary. In particle simulation, gyrokinetic schemes and the ' delta f' method have been found to give dramatic gains in some circumstances. Many of the newer results obtained withstand comparison with experimental observation, although it has not always proved possible to reach the extreme conditions found in tokamaks, especially when three-dimensional effects are important.