Cardiac and pulmonary physiology in patients with functionally univentricular hearts is markedly different from that found in the setting of the normal circulation. The physiology of both the heart and the lungs remains abnormal after palliative procedures, such as creation of systemic-to-pulmonary shunts, banding of the pulmonary trunk, or creation of the cavo-pulmonary connections. In this brief review, I will concentrate on two main aspects of physiology, namely oxygenation and haemodynamics. I will make comparisons between the normal circulation and the functionally univentricular circulation, the latter both before and after creation of a cavo-pulmonary connection. To finish, I will discuss the physiology of the cavo-pulmonary connection itself, and consider some clinical implications.