Fuel cells are likely to play a key role in any low-carbon economy. Solid oxide fuel cells (SOFCs) are currently capable of sustained and continuous operation on high-purity fuels, but they must demonstrate that they can overcome a number of challenges before they are commercially viable on a large scale. Fuels such as natural gas, and those derived from renewable sources such as gasified biomass, contain many contaminants, typically sulfur- and carbon-containing compounds. To address this it will be necessary to improve our understanding of failure modes in operating SOFCs, and act on this to reduce degradation rates. A combination of techniques will be needed to develop a rigorous approach to understanding and mitigating degradation. The intent of this article is to present a synopsis of the current state of the art in our understanding of the effect of carbon and sulfur on SOFC anodes. Emphasis is placed on the comparison between thermodynamic and kinetic models, and experimental validation of these. In particular the applicability of thermodynamic models to the study of such contaminants is questioned. Additionally the uses of multiscale kinetic models capable of predicting transient conditions are reviewed alongside recent analytical techniques necessary for their validation.