Periodic effects form the basis for progress in understanding the role of structure/function relationships in hydrodesulfurization (HDS). Theoretical results of Toulhoat, and Raybaud et al. based on ab initio calculations using density functional theory calculations as well as experimental results of Berhault et al. have recently confirmed the initial proposal of Pecoraro and Chianelli about the Sabatier principle interpretation for HDS activity either for transition metal binary bulk sulfides or for cobalt promotion Of MoS2-based catalysts. An optimum HDS activity corresponds to a moderate active site-organic sulfur-containing reactant interaction. An update is presented here with a special attention to the electronic foundations of the Sabatier principle as applied to HDS catalysis.