Mitochondrial/nuclear transfer (M/NT) to avoid the transmission of serious mitochondrial disease raises complex and challenging ethical, legal and social issues (ELSI). In February 2015, the United Kingdom became the first country in the world to legalize M/NT, making the heated debate surrounding this technology even more relevant. This critical interpretive review identified 95 relevant papers discussing the ELSI of M/NT, including original research articles, government-commissioned reports, editorials, letters to editors and research news. The review presents and synthesizes the arguments present in the literature in relation to the most commonly raised themes: terminology; identity, relationships and parenthood; potential harm; reproductive autonomy; available alternatives; consent; impact on specific interest groups; resources; “slippery slope”; creation, use and destruction of human embryos; and beneficence. The review concludes by identifying those ELSI that are specific to M/NT and by calling for follow-up longitudinal clinical and psychosocial research in order to equip future ELSI debate with empirical evidence.