Xenotransplantation using pigs as the transplant source has the potential to resolve the severe shortage of human organ donors. Although the development of relatively non-toxic immunosuppressive or tolerance-inducing regimens will be required to justify clinical trials using pig organs, recent advances in our understanding of the biology of xenograft rejection and zoonotic infections, and the generation of alpha1,3-galactosyltransferase-deficient pigs have moved this approach closer to clinical application. This Review highlights the major obstacles impeding the translation of xenotransplantation into clinical therapies and the potential solutions, providing a perspective on the future of clinical xenotransplantation.