The ultimate purpose of research in xenografting (cross-species transplantation) is successful transplantation of tissue and organs from animals to human patients. Success in the clinical application of xenografting would mean an end to the shortage of donor organs. Xenografts are classified as concordant or discordant, depending on rejection factors and histology. Several clinical attempts have been made since 1963, but success has been limited. However, great progress has been made in laboratory attempts; and the procedures should now be given clinical trials. This success has been due to the efficacy of many of the newly developed immunosuppressive drugs. Discordant xenografting is still problematic, and in this type of transplantation the most promising approach would seem to be with isolated cells or cell clusters.