A comprehensive overview of the models and methods employed in the rapidly advancing field of numerical ocean circulation modelling. For those new to the field, concise reviews of the equations of oceanic motion, subgridscale parameterization, and numerical approximation techniques are presented and four specific numerical models, chosen to span the range of current practice, are described in detail. For more advanced users, a suite of model test problems is developed to illustrate the differences among models, and to serve as a first stage in the quantitative evaluation of future algorithms. The list of references should make this a useful text for both graduate students and postdoctoral researchers in the marine sciences and in related fields such as meteorology, and climate and coupled biogeochemical modelling.