In most medical procedures, the benefit appears likely to exceed the risk by so much that detailed quantification of the risk is unnecessary. In some instances, however, it is important to attempt to estimate and compare the likely amount of the risk and of the benefit, to determine whether, or when, the use of the procedure is justified. This need arises in the use of radiological screening programmes for the early diagnosis of certain forms of cancer, to assess the age above which such a programme would save more lives by making early diagnoses than it would lose by inducing cancer in the tissues irradiated. It is also informative to estimate the levels of risk that might be involved in research studies involving radiation exposure. Conventional diagnostic and therapeutic procedures entail risks of fatality ranging over at least four orders of magnitude, and clearly relate to the urgency of the situations in which the procedures need to be used. Estimates of such risks are reviewed.