Donor organ availability has become a major limiting factor in the progress of allotransplantation. This, and advances in genetic engineering in pigs, have led to increasing interest in the use of xenogeneic organs. In view of the greater difficulty encountered in overcoming immune responses to xenografts than to allografts, the success of clinical xenotransplantation may depend on finding ways of inducing specific hyporesponsiveness, or tolerance, across xenogeneic barriers rather than by relying on nonspecific immunosuppressive agents. This review discusses the barriers to xenogeneic organ transplantation and the approaches that are being developed to overcome them, with the emphasis on methods that attempt to induce tolerance.