Pulmonary hypertension (PH) is a heterogeneous group of diagnoses including pulmonary vascular disease, left-sided heart failure, lung disease, and thromboembolic disease. Regardless of the cause, PH is often associated with increased morbidity and mortality. In systolic heart failure, the development of irreversible PH precludes cardiac transplantation because the risk of allograft right-ventricular failure and death is increased. In these cases, left ventricular assist devices (LVADs) can provide circulatory support and the potential to reverse PH. This chapter discusses the WHO classifications of PH and the associated diagnoses, mechanisms, and medical and surgical treatments for PH. It also discusses the strategies for reversing PH, the indications for selecting patients with PH for heart transplantation, and how exposure of the donor heart to elevated pulmonary pressures can affect the recipient. In many of these challenging patients, mechanical circulatory support as a bridge to candidacy has permitted successful cardiac transplantation.