In recent years there has been great interest in simulating theoretically the growth of an electrical discharge in a gaseous dielectric. The review is a general introduction to the subject of discharge simulation and summarises the advances that have been made in modern computational techniques which enable the growth of a discharge to be traced from its initiation until instantaneous currents of perhaps many amperes are attained. In the first place the general continuity equations which govern the growth of a discharge are set up together with the appropriate boundary conditions. The formal solutions to these equations are summarised for the case of uniform applied electric fields and low ionisation densities when the space-charge distortion of the fields is negligible. Simulation models are then developed which take into account space-charge distortion of the field and enable the axial and radial development of a discharge between plane parallel electrodes to be traced from its initiation until the transient glow regime in reached. A summary is also given of preliminary investigations into the modelling of discharge growth in nonuniform-field electrode geometries. Most of the simulation methods described assume that all charged particles come into instantaneous equilibrium with ionisation and transport coefficients determined by the local values of the ratio electric field/gas pressure. In the later stages of discharge growth and near electrode surfaces this assumption is no longer valid, and possible models for following ionisation growth in nonequilibrium regions such as the cathode-fall are discussed and compared with corresponding Monte-Carlo and Boltzmann methods.