According to many experts, the turning point in the development of genome editing technologies (GET) was 2012, when Feng Zhang and Jennifer Doudna independently proposed the adaptive bacterial immunity system CRISPR/Cas9 for editing the genome of living cells of eukaryotic organisms. Since then, the range of applications of CRISPR/Cas9 technology and related GET has continued to grow like an avalanche. Thus, new genetically modified microorganisms, plants, and animals have been created, the experimental studies on the genetic foundations of life have greatly expanded, and revolutionary approaches to therapy and prevention of incurable diseases have been developed. However, the indisputable advantages of GET are associated with high risks (real and potential) to the environment, human health, and society as a whole. Significant progress in the genome editing in eukaryotes has led to a rapid appearance of humans with an "improved" genome, despite the openly expressed opposition of leading scientists working in this field. Among them, David Baltimore, Paul Berg, Jennifer Doudna, George Church, and Martin Jinek are calling for a global suspension of work with human embryos until the technical, legal and ethical standards in this area are developed. There is an urgent need for the development of an unambiguous public position and improvement of the regulatory framework for the GET, including that in the Russian Federation; the present review attempts to address the urgent issue of GET-related regulations. We discuss various approaches to regulating the use of GET in medicine. We review legal acts and ethical recommendations around the world concerning the GET-mediated modification of the plant and animal genetic material for the purpose of creating medical products and drugs. We also address the sensitive issue of editing the genome of human cells (somatic or germ). Special attention is paid to the relevant legal and ethical standards exiting in the Russian Federation. The presented data allow for a better understanding of the current situation and the areas of further research into GET, where the development and implementation of regulatory standards are especially urgent.