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Analysis in terms of the relative operating characteristic (ROC) has recently been applied to several studies of medical decision-making, primarily to decisions based on imaging techniques. This paper presents a brief description of the ROC, and shows how it provides a measure of diagnostic accuracy that is free of judgmental bias. The results of medical studies are reviewed, and the main questions of theory and method that have arisen in the medical context are identified. Certain of these questions are basic to any psychophysical test, in which case an attempt has been made to present the best available answers. Other questions are of special medical importance and relevant reports are reviewed along with a description of current efforts to provide answers.