Workers employed in the nuclear energy industry and members of the general public living near nuclear facilities are exposed to low levels of ionising radiation as a result of the routine operation of these facilities. For the purposes of radiological protection, it is assumed that low doses of radiation confer a small increased risk of cancer upon the exposed individual and this is a major consideration in setting dose limits for workers and the general public. Quantitative estimates of radiation risk have been derived from epidemiological studies of groups exposed, on average, to high or moderate doses of radiation (such as the Japanese atomic bomb survivors), and appropriate assumptions are made for the application of such estimates to low dose conditions. There have been claims that the risks of cancer in nuclear industry workers, in their children, and in populations living around nuclear facilities have been grossly underestimated. Substantial evidence is now available from the epidemiological study of these groups. Studies of nuclear industry workforces demonstrate that currently accepted risk estimates are at about the right level, although a positive trend of leukaemia mortality with radiation dose, of a magnitude which is compatible with predictions, can be detected in the most statistically powerful workforce studies. The hypothesis that irradiation of fathers before the conception of their children materially increases the risk of childhood leukaemia has been largely discounted since it is biologically implausible and has found no support in studies using data independent of the study which generated the hypothesis. Increased levels of childhood leukaemia have occurred near certain nuclear facilities in the United Kingdom, but it is most unlikely that these are related to exposure to ionising radiation. Recent evidence suggests that these excesses are caused by a rare response to an infectious agent, which is enhanced under the unusual conditions of population mixing found in these communities. Similar excesses of childhood leukaemia have been found in other communities which have experienced unusual population mixing, but are not near nuclear facilities.