The carcinogenic effects of high levels of ionizing radiation are better understood than those of any other environmental agent. However, the somatic risk from low doses is highly disputed. The uncertainties stem from the fact that due to a multitude of confounding factors a direct estimation of small risks requires impracticably large samples. Therefore, risk estimates for low doses have to be derived indirectly by extrapolation from high-exposure data and are heavily dependent on assumptions about the shape of the dose-response curve. Although radiobiological theories tested mostly on in vitro systems predict a quadratic term in the dose-response equation, which should dominate the shape of the curve at least for sparsely ionizing radiation, the epidemiological data available are not yet sufficient to exclude the possibility of a purely linear relationship. In some cases, apparent thresholds may result from latent periods inversely related to dose. Besides depending on the quality of the radiation, the shape also seems to differ with the type of cancer induced The huge epidemiological data base on atomic bomb survivors, irradiated patients, miners, and other exposed groups can most consistently be fitted to a linear quadratic model For lung cancer in miners resulting from high linear energy transfer alpha radiation and for female breast cancer, the linear component seems to be dominant. A review of some highly publicized reports claiming a large cancer risk from low levels of radiation shows that their credibility is generally low and that most “effects” can be explained by the relatively large statistical fluctuations generally encountered in small samples