Computer-controlled polishing has introduced determinism into the finishing of high-quality surfaces, for example those used as optical interfaces. Computer-controlled polishing may overcome many of the disadvantages of traditional polishing techniques. The polishing procedure is computed in terms of the surface error-profile and the material removal characteristic of the polishing tool, the influence function. Determinism and predictability not only enable more economical manufacture but also facilitate considerably increased processing accuracy. However, there are several disadvantages that serve to limit the capabilities of computer-controlled polishing, many of these are considered to be issues associated with determination of the influence function. Magnetorheological finishing has been investigated and various new techniques and approaches that dramatically enhance the potential as well as the economics of computer-controlled polishing have been developed and verified experimentally. Recent developments and advancements in computer-controlled polishing are discussed. The generic results of this research may be used in a wide variety of alternative applications in which controlled material removal is employed to achieve a desired surface specification, ranging from surface treatment processes in technical disciplines, to manipulation of biological surface textures in medical technologies.