We have reviewed in this Brief the state of the art and the current development directions of the numerical methods at the core of Earth System Models. It is easy to see that, over the last 20 years, a much wider range of techniques has been proven to be applicable to oceanic and atmospheric flows than in the earlier stages of climate model development. The impressive increase in computational power is certainly one of the driving forces behind this change. It is very likely to yield in the near future models based on numerical methods that would not have been considered practically useful just a few years ago. Furthermore, massively parallel architectures have become the effective standard in supercomputing, thus imposing good scalability and strong data locality as essential requirements for any model to be applied extensively in this context.
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