CRISPR/Cas (clustered regularly interspaced short palindromic repeats linked to Cas nuclease) technology has revolutionized many aspects of genetic engineering research. Thanks to it, it became possible to study the functions and mechanisms of biology with greater precision, as well as to obtain genetically modified organisms, both prokaryotic and eukaryotic. The changes introduced by the CRISPR/Cas system are based on the repair paths of the single or double strand DNA breaks that cause insertions, deletions, or precise integrations of donor DNA. These changes are crucial for many fields of science, one of which is the use of animals (pigs) as a reservoir of tissues and organs for xenotransplantation into humans. Non-genetically modified animals cannot be used to save human life and health due to acute immunological reactions resulting from the phylogenetic distance of these two species. This review is intended to collect and summarize the advantages as well as achievements of the CRISPR/Cas system in pig-to-human xenotransplantation research. In addition, it demonstrates barriers and limitations that require careful evaluation before attempting to experiment with this technology.