The review paper presents current views on risks of incidence of neoplasms in persons exposed to power magnetic fields (PMFs) 50 Hz in the environment or at working posts. Cancer risks of power magnetic fields are small and doubtful, but there exist confirmed epidemiologic investigations that in children living in homes where PMF intensity exceeds 0.3-0.4 microT (0.24-0.32 A/m) an increased risk of certain types of leukemias can be observed. About one percent of children live under conditions of PMF exposure. Cancer morbidity in workers exposed to power magnetic fields is not unequivocally increased. Ten years ago, on the basis of available epidemiologic data, PMFs 50 Hz were listed as a possible carcinogenic agent (group 2B according to the IARC classification), which means lack of convincing evidence that PMFs pose cancer risks. The authors also discuss the binding regulations on the protection of the general population and workers against power magnetic fields and they conclude that existing permissible exposure levels are incompatible with exposure conditions, the present state of knowledge and health threats.