The paper reviews the problem of modelling short–wave scattering. Short waves are understood to be waves in which the wavelength is much smaller than any other parameters in the problem. The background to wave problems is briefly described. The major numerical methods for wave modelling, finite elements, finite differences, boundary integrals and their variants are then outlined. The recent developments in algorithms in these fields are then very briefly summarized, as an introduction to the more specialized papers to come.