Solid oxide fuel cells (SOFCs) are a rapidly emerging energy technology for a low carbon world, providing high efficiency, potential to use carbonaceous fuels and compatibility with carbon capture and storage. However, current state-of-the-art materials have low tolerance to sulfur, a common contaminant of many fuels, and are vulnerable to deactivation due to carbon deposition when using carbon-containing compounds. In this review we first study the theoretical basis behind carbon and sulfur poisoning, before examining the strategies towards carbon and sulfur tolerance used so far in the SOFC literature. We then study the more extensive relevant heterogeneous catalysis literature for strategies and materials which could be incorporated into carbon and sulfur tolerant fuel cells.