Wear particles are three-dimensional objects. Recent advances, accelerated by the application of computer technology, allow numerical characterization of particle shape in two dimensions. However, three-dimensional (3D) characterization of wear particle surface topography is still largely an unresolved problem. There are two issues associated with this problem, i.e., the acquisition of accurate wear particle surface topography data and the numerical description of 3D surface features. The usually small size of wear particles restricts the techniques that could be used to acquire accurate data from the particle surface. Surface profilometers, e.g., Talysurf, the instruments traditionally used in surface topography imaging, cannot be used because of the small size of particles. The limitation of an atomic force microscope is its relatively small vertical range, while the horizontal resolution of laser confocal or interferometric microscopes is too low to obtain accurate particle surface topography data. The application of a combination of SEM and stereoscopy techniques seems to alleviate this problem. 3D surface topography data obtained using this technique can be processed and presented in many different ways. The usefulness of various methods of surface data representation in visualization and numerical characterization of wear particle surfaces is discussed. One of the major difficulties associated with the characterization of surface topographies is the accurate description of surface spatial properties, i.e., their anisotropy and directionality. Recently, a specially modified Hurst Orientation Transform (HOT), to suit wear particle surface data, has been developed and applied to characterize the surface topography of particles. The Hurst coefficients are related to fractal dimensions and are a measure of surface roughness, i.e., a rougher surface is represented by lower Hurst coefficients. It was found that the modified HOT can be applied to reveal the surface anisotropy of wear particles. Although none of the other methods developed so far allow such a thorough characterization of wear particle surfaces as does the modified HOT, this method still does not provide a full description of the surface topography. Therefore, it appears that a totally different approach is needed in order to make a fundamental breakthrough in the characterization of wear particle surfaces. Since many of the complex structures observed in nature can be described and modelled by a combination of simple mathematical rules, it may be possible to describe the surface of a particle by a set of such rules. In our first attempt, a Partitioned Iterated Function System (PIFS) was applied to encode the wear particle surface topography information. This information can then be used to calculate the relevant surface descriptors. In this paper, an overview of recent advances and developments in the numerical characterization of wear particle surfaces is presented. (C) 1999 Elsevier Science S.A. All rights reserved.