This article considers recent progress in modelling the degradation of Fe9Cr steels exposed to high-temperature CO2. Computational modelling is used to rationalise the mechanism of the so-called breakaway oxidation, which is shown here to be associated with the carburisation of the underlying Fe9Cr substrate of finite dimensions. Oxidation kinetics, non-steady-state carburisation kinetics, and the mass transport mechanisms are covered. The theoretical and numerical/analytical challenges are discussed, with possible ways forward being suggested. Thus, we demonstrate that the software systems built on Prof. Hillert’s legacy are maturing rapidly towards engineering tools which can be used to anticipate the degradation of complex multicomponent alloys in engineering situations of relevance and significant complexity.