Xenotransplantation of porcine hearts has become a promising alternative to human allotransplantation, where organ demand still greatly surpasses organ availability. Before entering the clinic, however, feasibility of cardiac xenotransplantation needs to be proven, ideally in the life supporting orthotopic pig-to-nonhuman primate xenotransplantation model. In this review, we shortly outline the last three decades of research and then discuss in detail its most recent advances. These include the genetic modifications of donor pigs to overcome hyperacute rejection and coagulation dysregulation, new organ preservation methods to prevent perioperative xenograft dysfunction, experimental immunosuppressive and immunomodulatory therapies to inhibit the adaptive immune system and systemic inflammation in the recipient, growth control concepts to avoid detrimental overgrowth of the porcine hearts in nonhuman primates, and lastly, the avoidance of porcine cytomegalovirus infections in donor pigs. With these strategies, consistent survival of 6–9 months was achieved in the orthotopic xenotransplantation model, thereby fulfilling the prerequisites for the initiation of a clinical trial.