Heart transplantation remains the best treatment for terminal heat failure. Ischemic and idiopathic cardiomyopathies are the main indications. Contraindications are due to immunosuppressive treatment and fixed pulmonary hypertension. After clinical evaluation, the patient is put on the waiting list controlled by the French Biomedicine Agency. Acute rejection had decrease due to the improvement of immunosuppressive treatments. The incidence of severe acute rejection is 5%. Chronic rejection is the main cause of morbidity and mortality. The rate at 5 years is about 40-50%. Survival at one year is 80%. The rate of mortality per year is 4%. Survival at 5 and 10 years are respectively 65 and 50%.