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