Solid oxide fuel cells (SOFCs) offer great promise for the most efficient and cost-effective conversion to electricity of a wide variety of fuels such as hydrocarbons, coal gas, and gasified carbonaceous solids. However, the conventional Ni-YSZ (yttria-stabilized zirconia) anode is highly susceptible to deactivation (poisoning) by contaminants commonly encountered in readily available fuels, especially sulfur-containing compounds. Thus, one of the critical challenges facing the realization of fuel-flexible and cost-effective SOFC systems is the development of sulfur-tolerant anode materials. This perspective article aims at providing a comprehensive review of materials that have been studied as anodes for SOFCs, the electrochemical behavior of various anode materials in H2S-contaminated fuels, experimental methods for ex situ and in situ characterizations of species and phases formed on anode surfaces upon exposure to H2S-containing fuels, mechanisms for the interactions between H2S and anode surfaces as predicted from density functional theory (DFT) calculations, and possible strategies of minimizing or eliminating the effect of sulfur poisoning. While significant progress has been made in developing alternative anode materials with better sulfur tolerance, in probing and mapping electrode surface species relevant to sulfur poisoning, and in unraveling the mechanisms of H2S–anode interactions using both computational and experimental approaches, many challenges still remain to bridge the gaps between models at different scales or between theoretical predictions and experimental observations. An important new direction for future research is to develop a predictive multi-scale (from DFT to continuum) computational framework, through a rigorous validation at each scale by carefully-designed experiments performed under in situ conditions, for rational design of better sulfur-tolerant anode materials and structures for a new generation of SOFCs to be powered by readily available fuels.