Mutations induced by ionizing radiation in germ cells may affect future generations; mutations induced in somatic cells may damage the irradiated persons themselves, because radiation carcinogenesis is assumed to result from genetic damage induced in somatic cells. Since we are exposed mainly to low doses of ionizing radiation, both from natural and artificial sources, especially the dose dependence of radiation-induced mutations in the low-dose range is of interest. A review of recent studies on the induction of mutations by X-rays in human cells (in vitro) favors the hypothesis that in the low-dose range the dose dependence is linear, without a "threshold."