The present review provides an understanding of our current knowledge of the carcinogenic effect of low-dose radiation in man, and surveys the epidemiological studies of human populations exposed to nuclear explosions and medical radiation. Discussion centers on the contributions of quantitative epidemiology to present knowledge, the reliability of the dose-incidence data, and those relevant epidemiological studies that provide the most useful information for risk estimation of cancer induction in man. Reference is made to dose-incidence relationships from laboratory animal experiments where they may obtain, for problems and difficulties in extrapolation from data obtained at high doses to low doses, and from animal data to the human situation. The paper describes the methods of application of such epidemiological data for estimation of excess risk of radiation-induced cancer in exposed human populations and discusses the strengths and limitations of epidemiology in guiding radiation protection philosophy and public health policy.