The actuality of the research topic is dictated by the fact that organ transplantation is, in some cases, last hope for the patient, and a last resort for the doctor. Thus, in the attempt of physicians to save as many lives as possible, in the last century, they have been concerned with the discovery of new and new methods of treatment, and with the intense development of medical equipment and technology has been achieved transplantation of organs and tissues in human subjects. However, performing an such activity, besides the medical aspects, raises a number of ethical and moral issues. For the elaboration of the article have been used Various methods such as: analysis, synthesis, logic and comparative analysis. Finally, the author comes up with some suggestions that would be helpful in changing the attitude of the population to organ transplantation, as well as popularizing transplantation.