This paper is a review of recent advances accomplished in the field of hydrotreatment (HDT) sulfide catalysts and using theoretical approaches based on the density functional theory (DFT) combined with thermodynamic models and microkinetic models. We illustrate first numerous concepts of modem DFT simulation for a better understanding of the industrial Co(Ni)MoS active phases: localization and role of the promoter, electronic properties and morphological changes induced by the reaction conditions or by promoter addition. Then, it is shown how support effects can be modeled by DFT to provide new insights on the local structure and energy stability of the active phase-support interface, where characterization techniques reach their limits. The comparison between gamma-alumina and anatase-TiO2 supports is chosen as a relevant example. Finally, DFT simulations and microkinetic models help to rationalize "volcano-curve" type relationships between hydrodesulfurization (HDS) or hydrogenation (HYD) activities and the calculated sulfur-metal bond energy descriptor. This approach opens new routes to use systematic DFT simulations as a predictive tool. Perspectives for DFT simulations in the area of catalysis by sulfides are suggested. (C) 2007 Elsevier B.V. All rights reserved.