The hepatopulmonary syndrome (HPS) is defined as the triad of liver disease, intrapulmonary vascular dilatation, and abnormal gas exchange, and is found in 10–32% of patients with liver disease. Liver transplantation is the only known cure for HPS, but patients can develop severe posttransplant hypoxemia, defined as a need for 100% inspired oxygen to maintain a saturation of ≥85%. This complication is seen in 6–21% of patients and carries a 45% mortality. Its management requires the application of specific strategies targeting the underlying physiologic abnormalities in HPS, but awareness of these strategies and knowledge on their optimal use is limited. We reviewed existing literature to identify strategies that can be used for this complication, and developed a clinical management algorithm based on best evidence and expert opinion. Evidence was limited to case reports and case series, and we determined which treatments to include in the algorithm and their recommended sequence based on their relative likelihood of success, invasiveness, and risk. Recommended therapies include: Trendelenburg positioning, inhaled epoprostenol or nitric oxide, methylene blue, embolization of abnormal pulmonary vessels, and extracorporeal life support. Availability and use of this pragmatic algorithm may improve management of this complication, and will benefit from prospective validation.