A brief description of simple diffusion theory is given, followed by an outline of some of the experimental techniques used to obtain diffusion data. Care is taken to distinguish between methods which measure concentrations of ionised donors (or acceptors) and methods which measure atomic concentrations. An indication is then given of the way in which experimental results can be analysed. The remainder of the review is devoted to a description of some of the more important and interesting work which has been carried out in the III-V group of semiconductors. The diffusion of shallow donors is described, taking into account both group IV dopants, which can occupy either the group III or the group V site in the crystal and group VI dopants which primarily occupy the group V site. In both cases,examples are found in which the concentration of electrons does not correspond to that of atoms. The case of group II acceptors is then considered and the important Zn/GaAs system is described at some length. Recent work on the diffusion of the transition elements in GaAs and InP is then reviewed, indicating why this is of current interest in the semiconductor industry. Finally, diffusion in superlattices is described and an account is given of the interesting phenomenon of impurity-induced interdiffusion between layers. Throughout the review emphasis is laid upon the various diffusion mechanisms which have been proposed for diffusion in the III-V group of compounds.