Different organisms, cell types, and even similar cell lines can dramatically differ in resistance to genotoxic stress. This testifies to the wide opportunities for genetic and epigenetic regulation of stress resistance. These opportunities could be used to increas the effectiveness of cancer therapy, develop new varieties of plants and animals, and search for new pharmacological targets to enhance human radioresistance, for example, for -manned deep space expeditions. Based on the comparison of transcriptomic studies in cancer cells, in this review we propose that there is a high diversity of genetic mechanisms of development of genotoxic stress resistance. This review focused onpossibilities and limitations of the proposed regulation of the resistance of normal cells whole organisms to genotoxic and oxidative stress by overexpressing of stress-response genes. Moreover, the existing experimental data on the effect of such overexpression on the resistance of cells and organisms to various genotoxic agents has been analyzed and systematized. We suggest that the recent advances in the development of multiplex and highly customizable gene overexpression technology that utilizes the mutant Cas9 protein and the wealth of available data on gene functions and their signal networks open new opportunities for research in this field.