A large proportion of patients with failing heart, liver or kidney, do not receive the needed organ because of an insufficient number of organ donors. As a result of this shortage in allografts, pig xenografts have been considered as an alternative source of organs for transplantation. The major obstacle currently known to prevent pig to human xenotransplantation is the interaction between the human natural anti-Gal antibody and the a-gal epitope(Gal alpha 1-3Gal beta 1-4GlcNAc-R), abundantly expressed on pig cells. This epitopes is expressed on pig and other mammalian cells, but is absent in humans because of the evolutionary inactivation of the alpha 1, 3galactosyltransferase gene in ancestral primates. In this review, we describe the characteristics of anti-Gal and of the alpha-gal epitope, their role in inducing xenograft rejection and some of the theoretical approaches for preventing this rejection.