Genetically engineered sheep and goats represent useful models applied to proof of concepts, large-scale production of novel products or processes, and improvement of animal traits, which is of interest in biomedicine, biopharma, and livestock. This disruptive biotechnology arose in the 80s by injecting DNA fragments into the pronucleus of zygote-staged embryos. Pronuclear microinjection set the transgenic concept into people's mind but was characterized by inefficient and often frustrating results mostly because of uncontrolled and/or random integration and unpredictable transgene expression. Somatic cell nuclear transfer launched the second wave in the late 90s, solving several weaknesses of the previous technique by making feasible the transfer of a genetically modified and fully characterized cell into an enucleated oocyte, capable of cell reprogramming to generate genetically engineered animals. Important advances were also achieved during the 2000s with the arrival of new techniques like the lentivirus system, transposons, RNA interference, site-specific recombinases, and sperm-mediated transgenesis. We are now living the irruption of the third technological wave in which genome edition is possible by using endonucleases, particularly the CRISPR/Cas system. Sheep and goats were recently produced by CRISPR/Cas9, and for sure, cattle will be reported soon. We will see new genetically engineered farm animals produced by homologous recombination, multiple gene editing in one-step generation and conditional modifications, among other advancements. In the following decade, genome edition will continue expanding our technical possibilities, which will contribute to the advancement of science, the development of clinical or commercial applications, and the improvement of people's life quality around the world.