Criteria for assessing the effectiveness of a medical screening program are difficult to define; medical knowledge and screening procedures change rapidly, and self-selection at medical screens is unavoidable. This article discusses these and other basic issues in evaluation of medical screening programs with particular reference to results from the HIP breast cancer study. In addition, the article reviews various statistical models that describe the processes of disease and screening. The models are shown to be statistically indistinguishable in practice because of the small sample sizes typically available in medical screening trials. Finally the article suggests incorporating knowledge from clinical trials and from studies of robustness into statistical models designed to identify reasonable strategies for screening.