Fontan palliation for the single ventricle results in a challenging and delicate physiological state. At rest, the body adapts to a low cardiac output and high systemic venous pressure. However, when physiological demands increase, such as in the case of exercise or pregnancy, this delicate physiology struggles to adapt due to the inability of the heart to pump blood into the lungs and the consequent lack of augmentation of the cardiac output.Due to the advances in paediatric cardiology, surgery and intensive care, today most patients born with congenital heart disease reach adulthood. Consequently, many women with a Fontan circulation are becoming pregnant and so far data suggest that, although maternal risk is not high, the outcomes are poor for the foetus. Little is known about the reasons for this disparity and how the Fontan circulation adapts to the physiological demands of pregnancy.Here we review current knowledge about pregnancy in Fontan patients and explore the potential role of computational modelling as a means of better understanding this complex physiology in order to potentially improve outcomes, particularly for the foetus.