Background: Mitochondrial DNA (mtDNA) diseases are a group of maternally inherited genetic disorders caused by a lack of energy production. Currently, mtDNA diseases have a poor prognosis and no known cure. The chance to have unaffected offspring with a genetic link is important for the affected families, and mitochondrial replacement techniques (MRTs) allow them to do so. MRTs consist of transferring the nuclear DNA from an oocyte with pathogenic mtDNA to an enucleated donor oocyte without pathogenic mtDNA. This paper aims to determine the efficacy, associated risks, and main ethical and legal issues related to MRTs. Methods: A bibliographic review was performed on the MEDLINE and Web of Science databases, along with searches for related clinical trials and news. Results: A total of 48 publications were included for review. Five MRT procedures were identified and their efficacy was compared. Three main risks associated with MRTs were discussed, and the ethical views and legal position of MRTs were reviewed. Conclusions: MRTs are an effective approach to minimizing the risk of transmitting mtDNA diseases, but they do not remove it entirely. Global legal regulation of MRTs is required.