Organ transplantation is in many cases the preferred treatment for the chronic failure of the major organs. There has been considerable success in preventing the rejection of transplanted organs, and further improvements in the outcome of transplantation are in prospect. However, the main limitation on the fullest possible use of organ transplantation is the shortage of donated human organs. One solution to this problem would be xenotransplantation, the use of animals instead of humans as the source of organs and tissues for transplant. The immunological barriers to this procedure are now well defined and this review describes the various strategies that are being developed to try to overcome them.