This article is a review of foreign works on the study of radioactive contamination of the atmosphere due primarily to diffusion of fission fragments from atomic tests. Several properties of fission fragment activity, namely its decay rate and the composition of its radiation, are considered, and methods are described for monitoring the fallout from the atmosphere and calculating the resulting radiation dose. The dose is almost everywhere much less than the permissible limit. At several places, however, fallout densities and activity concentrations are observed which are close to the allowable limit. A method for constructing the trajectories of air masses is briefly described, and it is shown that radioactive clouds migrate over the whole world, producing a radioactive layer in the atmosphere at an altitude of 8–12 km consisting primarily of the long-lived nuclides Sr90, Ce144, and Pu239. Of the fission fragments contaminating the earth's surface the most dangerous is Sr90 which has the property that it accumulates in the organisms of domesticated animals and thus enters the human organism. The radiation level at points fat from the test areas is at present far below the allowable limit in the sense of the possible occurrence of somatic diseases, although even at the present radiation level, effects on posterity cannot be excluded.