Radiation is a carcinogen, interacting with DNA to produce a range of mutations. Irradiated cells also show genomic instability, as do adjacent non-irradiated cells (the bystander effect); the importance to carcinogenesis remains to be established. Current knowledge of radiation effects is largely dependent on evidence from exposure to atomic bomb whole body radiation, leading to increases in a wide range of malignancies. In contrast, millions of people were exposed to radioactive isotopes in the fallout from the Chernobyl accident, within the first 20 years there was a large increase in thyroid carcinoma incidence and a possible radiation-related increase in breast cancer, but as yet there is no general increase in malignancies. The increase in thyroid carcinoma, attributable to the very large amounts of iodine 131 released, was first noticed in children with a strong relationship between young age at exposure and risk of developing papillary thyroid carcinoma (PTC). The extent of the increase, the reasons for the relationship to age at exposure, the reduction in attributable fraction with increasing latency and the role of environmental factors are discussed. The large number of radiation-induced PTCs has allowed new observations. The subtype and molecular findings change with latency; most early cases were solid PTCs with RET-PTC3 rearrangements, later cases were classical PTCs with RET-PTC1 rearrangements. Small numbers of many other RET rearrangements have occurred in 'Chernobyl' PTCs, and also rearrangement of BRAF. Five of the N-terminal genes found in papillary carcinoma rearrangements are also involved in rearrangements in hematological malignancies; three are putative tumor suppressor genes, and two are further genes fused to RET in PTCs. Radiation causes double-strand breaks; the rearrangements common in these radiation-induced tumors reflect their etiology. It is suggested that oncogenic rearrangements may commonly involve both a tumor-suppressor gene (or a DNA repair gene) as well as an oncogene. Involvement of two relevant genes would give a greater chance of progression and a shorter latency than a single-gene mutation. More information is needed on germline mutations conferring susceptibility to radiation-induced PTCs, particularly DNA repair genes. The radiation exposure to the fallout after Chernobyl was very different from the whole body radiation after the atomic bombs. The type and molecular pathology of the thyroid tumors is changing with increasing latency, long latency tumors in other organs could occur in the future. A comprehensive follow up must continue for the lifetime of those exposed.