In 2008, the Kinderkrebs in der Umgebung von KernKraftwerken (KiKK) study in Germany reported a 60% increase in solid cancer incidence and a 120% increase in leukaemia incidence among children living within 5 km of all German nuclear power stations. The study has triggered debates as to the cause(s) of these increased cancers. This article reports on the findings of the KiKK study; discusses past and more recent epidemiological studies of leukaemias near nuclear installations around the world, and outlines a possible biological mechanism to explain the increased cancers. In essence, this suggests that doses to embryos/foetuses in pregnant women from environmental emissions from nuclear power plants (NPPs) may be larger than suspected, and that haematopoietic tissues may be considerably more radiosensitive in embryos/foetuses than in children and adults. The article concludes with recommendations for further research.