Agrave problem of modern oil refining industry is continuous deterioration of the produced oil quality, on the one hand, and increase in the demand for motor fuels, on the other hand. This necessitates processing of heavy oil feedstock with high contents of sulfur, nitrogen and metals and the atmospheric residue. This feedstock is converted to light oil products via hydrogenation processes catalyzed by transition metal compounds, first of all, cobalt-or nickel-promoted molybdenum and tungsten compounds. The processing involves desulfurization, denitrogenation and demetallization reactions as well as reactions converting heavy hydrocarbons to lighter fuel components. The review discusses the mechanisms of reactions involved in the heavy feedstock hydroprocessing, the presumed structure and state of the catalytically active components and methods for the formation of supports with the desired texture. Practically used and prospective approaches to catalytic upgrading of heavy oil feedstock as well as examples of industrial processing of bitumen and vacuum residues in the presence of catalysts are briefly discussed. The bibliography includes 140 references.