Modern transplantology is one of the most complex spheres of current health care. Its development has created and continues to create bioethical and legal problems that can be addressed differently in different societies. In the article the authors identify the main problems currently relevant, Such as the definition of death and its diagnosis, issues of consent to the removal of organs and tissues from the body, Issues of organ and tissue costs and ways to reward donors, Transplantation tourism, criminalization, smuggling, sale and sale of organs and tissues, Moral problems affecting the bioethical principles of "good and harm," do not harm, " "Human vulnerability and respect for integrity," human rights and human dignity, " "Autonomy and individual responsibility," consent, "equality, justice and equity," non-discrimination and stigmatization, " "Solidarity and cooperation," social responsibility and health, "benefit-sharing."