Transplantation of organs across species (xenotransplantation) is being considered to overcome the shortage of human donor organs. However, unmodified pig organs undergo an anti body-mediated hyperacute rejection that is brought about by the presence of natural antibodies to Gal alpha(1,3)Gal, which is the major carbohydrate xenoantigen. Genetic modification of pig organs to remove most of the Gal alpha(1,3)Gal epitopes has been achieved, but the human immune system may still recognize residual lipid-linked Gal alpha(1,3) Gal carbohydrates, new (cryptic) carbohydrates or additional non-Gal alpha(1,3) Gal carbohydrate xenoantigens. The structural basis for lectin and antibody recognition of Gal alpha(1,3)Gal carbohydrates is starting to be understood and is discussed in this review. Antibody binding to Gal alpha(1,3)Gal carbohydrates is predicted to primarily involve end-on insertion of the terminal alpha Gal residue, but it is possible that groove-type binding can occur, as for some lectins. It is likely that similar antibody and lectin recognition will occur with other non-Gal alpha(1,3)Gal xenoantigens, which potentially represent new barriers for pig-to-human xenotransplantation.