The surgical repair of congenital heart disease often involves significant modifications to the circulatory tree. Resections, reconstructions, graft insertions and the deployment of implants and biomedical devices have an impact on local and systemic haemodynamics, which may be difficult to foresee or to assess quantitatively by clinical investigation alone. Mathematical models can be employed to visualise, estimate or predict events and physical quantities that are difficult to observe or measure, and can be successfully applied to the study of the pre- and post-operative physiology of cardiovascular malformations. This paper analyses the potentialities of computation fluid dynamics in this respect, outlining the method, its requirements and its limitations. Examples are given of lumped parameter models, axi-symmetric models, three-dimensional models, fluid-structure interaction simulations and multiscale computing applied to total cavo-pulmonary connection, aortic coarctation and aortic arch reconstruction.