The transfer of nuclear genomic DNA from a cell to a previously enucleated oocyte or zygote constitutes one of the main tools for studying epigenetic reprogramming, nucleus-cytoplasm compatibility, pluripotency state, and for genetic preservation or edition in animals. More than 50 years ago, the first experiences in nuclear transfer began to reveal that factors stored in the cytoplasm of oocytes could reprogram the nucleus of another cell and support the development of an embryo with new genetic information. Furthermore, when the nuclear donor cell is an oocyte, egg, or a zygote, the implementation of these technologies acquires clinical relevance for patients with repeated failures in ART associated with poor oocyte quality or mitochondrial dysfunctions. This review describes the current state, scope, and future perspectives of nuclear transfer techniques currently available for assisting mammal reproduction.