Some 10(9) years ago the first living organisms took form in a radioactive environment (telluric radioactivity), which was itself bombarded by radiations coming from the cosmos (cosmic rays). External and internal exposure, which is nowadays incurred from these radiations, results in a mean absorbed dose of about 2.5 mSv per year for the average world population. This mean absorbed dose can obviously be slightly different from one population to another one depending on the geology and the altitude. The discovery of radioactivity and the very numerous applications that were done have added some extra dose to these natural exposures. This increment, less than 2 % of the natural exposure for electro-nuclear power plants, can reach, even exceed, some mGy in medical applications without mentioning therapeutic uses for which the absorbed doses are very large, Air travelling increases at very high altitudes, holidays in mountain resorts, and some new technologies have also their part in the increase of human exposure. Of course, all living organisms have developed very powerful defense systems against free radicals mainly those arising from oxygen consumption (SOD, glutathion peroxydase, catalase, etc...), and in comparison the adaptive response due to very low radiation exposure, if actual, must therefore be a little bit limited because of the very small number of free radicals involved. Cells must have developed very efficient DNA repair systems in order to keep unaltered their genetic information.