Heart transplant recipients with secondary pulmonary hypertension (PH) are prone to acute right ventricular (RV) graft failure after orthotopic heart transplantation (oHTX). A suitable donor heart of a healthy individual is not adapted to elevated RV afterload caused by PH. In contrast, the majority of potential heart transplant recipients suffer from chronic left ventricular (LV) failure. LV insufficiency requires elevated filling pressures to maintain cardiac output (CO), (LV backwards failure) and causes systemic hypotension (LV forward failure) which induces systemic and pulmonary vasoconstriction. This increases systemic (SVR) and pulmonary vascular resistance (PVR), induces RV hypertrophy and secondary PH. After oHTX, the unadapted transplanted RV is exposed to the recipients PVR, RV afterload mismatch results in acute RV failure when the patient is weaned from cardiopulmonary bypass. RV volume overload, dilatation and structural damage are followed by RV failure and death. The preoperative estimation of PVR and of the reactivity of the pulmonary vascular bed to pulmonary vasodilators permits the selection of patients with reversible PH that are still suitable for oHTX. Many attempts failed to define a clear borderline beyond which oHTX is not feasible. In fact, RV failure after oHTX is caused by both, the elevated RV afterload of the recipient and by insufficient RV performance. Reduction of RV afterload by pulmonary vasodilator therapy reduces the risk of RV failure resulting from RV forward failure. The risk of inadequate myocardial function remains.