In this paper some of the issues associated with the application of computational fluid dynamics (CFD) to the design of prosthetic heart valves are discussed. The intentions are to emphasise that, for best effect, the analysis should integrate smoothly into the design process, and to illustrate the usefulness of the technique in providing detailed spatial and temporal resolution of quantities that are otherwise difficult to measure. The vehicle for the discussion is a chronological review of some valve analyses performed by the Sheffield group over the period from 1990 to 1994.