The important theoretical works that have been performed on hydrotreating catalysis within the last 10 years are reviewed. The active phase of these catalysts are generally constituted of MoS2 crystallites, promoted by cobalt or nickel and deposited on large area supports such as alumina. It is well admitted that the active site of the catalyst is located on the edges of the MoS2 particles. The review then focuses first on the sulfur stoechiometry of the edges Of MoS2 crystallites for both the promoted and unpromoted systems. It is shown, taking into account the gas phase surrounding the catalysts and the temperature, that on the metallic edge all the molybdenum atoms are saturated while on the sulfur edge they are in a four-fold tetrahedral coordination. This first part leads to propositions on the nature of the active surface that are confronted with experimental data. The influence of hydrogen on the stability of different surfaces is then discussed as well as H-2 activation and hydrogen mobility on the different edges. In a final part, results on the adsorption and on the determination of the desulfurization reaction pathways for different types of molecules such as thiols, thiophene and polyaromatic sulfur-containing compounds are presented and discussed. (C) 2007 Elsevier B.V. All rights reserved.