The Fontan operation, originally described for the surgical management of tricuspid atresia, is now the final surgery in the strategy of staged palliation for a number of different forms of congenital cardiac disease with a functionally univentricular heart. Despite the improved technical outcomes of the Fontan operation, staged palliation does not recreate a normal physiology. Without a pumping chamber delivering blood to the lungs, the cardiovascular system is less efficient; cardiac output is generally diminished, and the systemic venous pressure is increased. As a result, patients with "Fontan physiology" may face a number of rare but potentially life-threatening complications including hepatic dysfunction, abnormalities of coagulation, protein-losing enteropathy, and plastic bronchitis. Despite the staged palliation resulting in remarkable survival, the possible complications for this group of patients are complex, involve multiple organ systems, and can be life threatening. Identifying the mechanisms associated with each of the rare complications, and developing strategies to treat them, requires the work of many people at many institutions. Continued collaboration between sub-specialists and between institutions will be required to optimise the care for this group of survivors with functionally univentricular hearts.