We present density functional theory (DFT) calculations of reaction pathways for both the hydrogenation (HYD) and direct desulfurization (DDS) routes in the hydrodesulfurization (HDS) of thiophene over the different MoS2 edge structures, which will dominate under typical HDS reaction conditions. Contrary to the generally accepted view, we find that the HYD reaction path, which involves hydrogenation to 2-hydrothiophene followed by hydrogenation to 2,5-dihydrothiophene and subsequent SC scission, can occur at the equilibrium Mo(101¯0) edge without the creation of coordinatively unsaturated Mo edge sites. This is related to the presence of the metallic-like brim sites also observed in previous STM studies. It is found that the HYD reaction pathway also can occur at the S(1¯010) edge. At this edge, the equilibrium edge structure itself is not active, and sulfur vacancies must be created for the reaction to proceed. It is found that the effective energy barrier for vacancy creation depends on the H2 partial pressure. The sulfur vacancies at the S(1¯010) edge are also found to be active sites for the DDS pathway. This pathway does involve an initial hydrogenation step to 2-hydrothiophene, followed by SC scission. Analyzing the relative stabilities of reactants and intermediates suggests that a catalytic cycle may involve elementary steps that start at one type of edge and are completed at the other; for example, many intermediates are more stable at the S edge. The regeneration of the active sites is found to be a crucial step for all of the reaction pathways, and the importance of reactions at Mo brim sites is related to the observation that regeneration is least activated here. It is proposed that an important activity descriptor is the minimum energy required to either add or remove S from the different equilibrium edge structures.