Late-onset effects of exposure to ionising radiation on the human body have been identified by long-term, large-scale epidemiological studies. The cohort study of Japanese survivors of the atomic bombings of Hiroshima and Nagasaki (the Life Span Study) is thought to be the most reliable source of information about these health effects because of the size of the cohort, the exposure of a general population of both sexes and all ages, and the wide range of individually assessed doses. For this reason, the Life Span Study has become fundamental to risk assessment in the radiation protection system of the International Commission on Radiological Protection and other authorities. Radiation exposure increases the risk of cancer throughout life, so continued follow-up of survivors is essential. Overall, survivors have a clear radiation-related excess risk of cancer, and people exposed as children have a higher risk of radiation-induced cancer than those exposed at older ages. At high doses, and possibly at low doses, radiation might increase the risk of cardiovascular disease and some other non-cancer diseases. Hereditary effects in the children of atomic bomb survivors have not been detected. The dose-response relation for cancer at low doses is assumed, for purposes of radiological protection, to be linear without a threshold, but has not been shown definitively. This outstanding issue is not only a problem when dealing appropriately with potential health effects of nuclear accidents, such as at Fukushima and Chernobyl, but is of growing concern in occupational and medical exposure. Therefore, the appropriate dose-response relation for effects of low doses of radiation needs to be established.