Anesthesiologists face enormous challenges in patients with pulmonary hypertension(PH) and right heart failure who have increased risk of cardiovascular adverse events and mortality during the perioperative period. This article will review the anesthetic management of those patients with PH and right heart failure, including the pathophysiological changes, the preoperative assessment and management, and how to avoid the increase of perioperative pulmonary vascular resistance and ensure the right ventricular oxygen supply/demand balance.