The increasing shortage of human cadaveric organs for purposes of transplantation has become the critical limiting factor in the number of transplants performed each year. Some of this deficit is being met by the use of organs or partial organs from living donors, but this source is insufficient. Xenotransplantation—the transplantation of organs between species, namely from the pig to human—could provide a solution if immunologic and other associated problems could be solved. When a pig organ is transplanted into a primate, hyperacute rejection, induced by anti-pig antibody and mediated by complement and the coagulation system, develops rapidly. This immediate problem can now be overcome, but the return or persistence of anti-pig antibody leads to a delayed form of humoral rejection, acute humoral xenograft rejection, which leads to destruction of the organ within days or weeks. We review the various approaches being investigated to overcome this barrier. Whether they will also prevent subsequent acute cellular rejection remains unknown. Brief mention is made of the potential physiologic incompatibilities between pig and human organs, as well as the microbiologic safety aspects of xenotransplantation. Finally, the question of patient and societal acceptance of xenotransplantation is discussed.