© 2015 IJS Publishing Group Limited. Binding of natural anti-pig antibodies in humans and nonhuman primates to carbohydrate antigens expressed on the transplanted pig organ, the most important of which is galactose-α1,3-galactose (Gal), activate the complement cascade, which results in destruction of the graft within minutes or hours, known as hyperacute rejection. Even if antibody is removed from the recipient's blood by plasmapheresis, recovery of antibody is associated with acute humoral xenograft rejection. If immunosuppressive therapy is inadequate, the development of high levels of T cell-dependent elicited anti-pig IgG similarly results in graft destruction, though classical acute cellular rejection is rarely seen. Vascular endothelial activation by low levels of anti-nonGal antibody, coupled with dysregulation of the coagulation-anticoagulation systems between pigs and primates, leads to a thrombotic microangiopathy in the graft that may be associated with a consumptive coagulopathy in the recipient. The most successful approach to overcoming these barriers is by genetically-engineering the pig to provide it with resistance to the human humoral and cellular immune responses and to correct the coagulation discrepancies between the two species. Organs and cells from pigs that (i) do not express the important Gal antigen, (ii) express a human complement-regulatory protein, and (iii) express a human coagulation-regulatory protein, when combined with an effective immunosuppressive regimen, have been associated with prolonged pig graft survival in nonhuman primates.