The morphology of surfaces, depending on the nature of their environment, may be altered by erosional and/or accretional processes. Analytic description of the changing topography is possible through a knowledge of a locally variable parameter, which is the surface motion velocity in an arbitrarily specified direction. For sputter-related processes in which this parameter is spatially and temporally invariant over specific regions of a surface (e.g. ion milling, reactive-ion etching), the evolution of those regions may be forecast by geometric methods. Inhomogeneity of this parameter, which would generally result from the secondary and tertiary effects of ion irradiation, tenders evolution predictable only by iterative computer techniques. This paper summarises the status of analytic, geometric and computer methods of macroscopic surface simulation and notes the suitability of computer methods for simulation at the atomic scale.