© 2016 The Society of Thoracic Surgeons. If pig hearts could be transplanted successfully into patients with end-stage cardiac failure, the critical shortage of hearts from deceased human donors would be overcome. The several attempts at cardiac xenotransplantation carried out in the 20th century, usually with hearts from nonhuman primates (NHPs), are reviewed, as are the surgical techniques used in experimental heart transplantation in animals. For a number of reasons, the pig has been selected as the potential source of organs for clinical transplantation. The major pathobiological barriers that the pig presents, and progress in overcoming these barriers either by genetic engineering of the pig or by the administration of novel immunosuppressive agents, are described. Currently, non-life-supporting pig heterotopic heart transplantation in NHPs has extended to more than 2 years in 1 case, with life-supporting orthotopic heart transplantation of almost 2 months. Future approaches to resolve the remaining problems and the selection of patients for the initial clinical trials are briefly discussed.