Organ transplantation has evolved to become as gold standard therapy for patients with end-stage heart and/or pulmonary diseases. When medical or temporary circulatory supportive treatment modalities cannot ensure a patient’s survival and improve quality of life, the only approach may be isolated heart or lung transplantation, or combined transplantation. The main indication for heart transplantation is reversible pulmonary dysfunction with irreversible right heart failure; similarly, isolated irreversible pulmonary dysfunction resulting temporary right heart dysfunction requires isolated lung transplantation. However, irreversible right heart failure combined with irreversible pulmonary dysfunction requires heart–lung transplantation. The last two decades have seen the resolution of many technical problems and the refinement of surgical techniques for heart and lung transplantation, but problems remain for heart–lung transplantation because of complications such as major bleeding, nerve injuries, and graft failure. Patients with dominant right ventricular failure referred to heart transplantation usually suffer from the left-sided heart failure, primary pulmonary hypertension, and congenital heart diseases; however, the frequency of isolated right heart failure with structural abnormalities has also been increasing recently. Despite regular revisions of the transplantation guidelines that have resulted in annual increases in recipient pool, the number of donors has not increased sufficiently. Advances in the fields of immunosuppression, infection prophylaxis, and surgical techniques have improved surgical outcomes and long-term survival rates. Future improvements in organ donation could increase the donor numbers and improve donor–recipient immunologic matching and the allocation of organs. Biomechanical and biotechnological advancement in long-term ventricular assist devices may prolong survival and improve the quality of life; however, although mechanical circulatory support technology is improving, transplantation remains the sole effective treatment for irreversible right heart pathologies.