The ocean plays an essential role in determining aspects of the climate through its influence on coupled processes involving the atmosphere, cyrosphere and biogeochemistry, including budgets of heat and carbon dioxide and sea-level rise. Here, the key developments in ocean modelling over the past 20 years are reviewed and the prospects for the next 20 years are outlined, considering a hierarchy of idealized, conceptual and realistic modelling frameworks. It is emphasized that any long-term modelling strategy needs to be underpinned and complemented by fundamental theoretical and observational research activities. The need to be aware of the societal and technological drivers that will shape future research directions is also articulated.