A review of literature data regarding the heritable effects in offspring due to parents’ contact with mutagenic risk factors is presented. Studies on various factors of adverse effects on the hereditary apparatus, including chemical, infectious, physical and biological, are considered. The influence of smoking and parents’ age on the occurrence of de novo mutations is shown. Particular attention is paid to the review of publications on the role of the radiation factor in the genesis of hereditary disorders in offspring. Development stages of radiation genetics, the evolution of conception about radiation harm are described. The results of experimental, cytogenetic, molecular genetic, epidemiological studies analyzing the contribution of parental exposure to inherited pathology in progeny are presented. Special attention is paid to the “untargeted” effects of radiation and studies which prove the possibility of transgenerative transmission of genome instability are presented. The special contribution of studies on the cohort of atomic bomb victims offspring in Hiroshima and Nagasaki, which is considered as the main scientific platform for radiation risk assessment, is noted. There are articles about the offspring of persons who underwent therapeutic exposure, who had professional contact with ionizing radiation, who were exposed to radiation as a result of the Chernobyl accident, nuclear weapons tests at the Semipalatinsk test site, chronic radiation in the radioactively contaminated territory of the Techa river, areas with naturally increased radioactivity. As a result, it was noted that, despite numerous confirmations of radiation-induced effects in offspring obtained within experimental and molecular genetic studies, the results of epidemiological studies remain controversial. Possible reasons for these discrepancies are considered. An idea of views evolution regarding heritable effects in the international system of radiation safety is given. A new approach of the International Commission on Radiological Protection to heritable effects is described; the dynamics of tissue weighting factors for gonads in the assessment of effective radiation dose is shown. Methods for evaluating heritable effects are presented: the direct method and the doubling dose method. Attention is focused on the uncertainties that remain in the modern assessment of radiation genetic damage. The necessity of further study of radiation-induced heritable effects is shown. The perspective directions of studying the heritable effects are considered. The possibility of the analysis of heritable effects is described using the example of a cohort of the Mayak Production Association workers’ offspring – the country’s first nuclear industry enterprise.