Organ transplantation is limited by the number of cadaveric human donor organs that become available. Xenotransplantation--the transplantation of organs and tissues between animal species--would supply an unlimited number of organs and offer many other advantages. The pig has been identified as the most suitable donor animal. Pig organs, when transplanted into humans or nonhuman primates, are, however, rejected hyperacutely within minutes by antibody-mediated complement activation. Human anti-pig antibodies have been identified as being directed against Gal alpha1-3galactose epitopes on pig vascular endothelium. Major efforts are being made to overcome this hyperacute rejection. Methods being investigated include (i) depletion or inhibition of recipient antibodies or complement, (ii) development of transgenic pigs that do not express the alphaGal epitope and/or express a human complement inhibiting protein (e.g. DAF), and (iii) development of immunological tolerance to pig organs in the recipient. If complement activation is prevented, e.g. by inhibition of complement activation by cobra venom factor, soluble complement receptor 1 or by the use of hDAF transgenic pig organs, then "delayed xenograft rejection" occurs and is again believed to be largely antibody-dependent. Experimental pig-to-primate organ xenotransplantation is now, however, resulting in transplant function for days and weeks rather than minutes, and there is therefore optimism that we are on the threshold of a new era in the field of the transplantation of vital organs.