The reduced availability of human donor hearts compared with the needs of patients with advanced heart failure refractory to medical therapy has promoted the search for therapeutic alternatives to cardiac allografts. Porcine heart xenotransplantation represents one of the most promising frontiers in this field today. From the first researches in the 1960s to today, the numerous advances achieved in the field of surgical techniques, genetic engineering and immunosuppression have made it possible at the beginning of 2022 to carry out the first swine-to-human heart transplant, attaining a survival of 2 months after surgery. The main intellectual and experimental stages that have marked the history of xenotransplantation, the latest acquisitions in terms of genetic editing, as well as the improvement of immunosuppressive therapy are discussed analytically in this article in order to illustrate the underlying complexity of this therapeutic model.