Hydrotreating processes in petroleum refining were introduced more than 50 years ago for the removal of sulfur and nitrogen. The sulfided cobalt-molybdenum catalyst, together with its near relatives, is still widely used. Two oil crises made it clear that pretroleum reserves are not inexhaustible and we shall be compelled to exploid less satisfactory sources with high sulfur and nitrogen making hydrotreating even more important. This review is particularly timely for the reason that only recently has a detailed understanding of process chemistry and catalyst structure been obtained. The authors concentrate on the catalytic chemistry of the processes, dealing in some detail with the structure of the most important types of catalysts and the relationship of structure to activity.