Ethical and legal consensus in our country bases the practice of donations and transplants on different ethical principles, which are contained in the legislation, closely conforming to the four principles of principialist bioethics: autonomy, beneficence, non-maleficence, and justice. The level of donations achieved in our milieu might, in fact, be related to a strict respect for these principles by the health professionals, as well as to the excellent organisation of the transplant world. Many scientific, technical and ethical challenges have had to be met to reach the present state of the transplant. And there are many current challenges. The article only analyses some of these due to their technical, ethical and social repercussions: organ transplants involving a live donor, the public request for organs, the organ market, the transplant of non-vital organs (basically the face transplant), the use of stem cells and the banks of umbilical cord cells. The aim of the article is to state the ethical problems raised by these new practices, in order to lay the foundations for a moral deliberation that must necessarily involve the whole of society.