In France, since the approval of the first bioethics laws in 1994, the principle of the anonymity of sperm donors has prevailed. This choice is regularly challenged, namely by children who have been conceived under these conditions and have now reached adulthood. In this paper, we will briefly describe the reasons that led practitioners of assisted reproduction to endorse the anonymity principle in 1994. Secondly, we will elaborate on the reasons why this principle is becoming so controversial today. Finally, we shall examine two possible outcomes of the debate, highlighting their respective legitimacy as well as their consequences, as far as the rights of children, the notion of the family, and medical practice are concerned.