A process for upgrading, or refining, high sulfur containing heavy hydrocarbon crude oil to a lighter oil having a lower sulfur concentration and, hence a higher value product, is disclosed. The process includes reacting the high sulfur heavy hydrocarbon crude oil in the presence of a catalyst and low pressure hydrogen to produce a reaction product stream from which the light oil is recovered. Part of the reaction product is separated and subjected to further upgrading to produce a lower sulfur oil product for application as distillate fuels. The upgrading process also produces residual oil that is suitable for making olefins, carbon fiber or road asphalt. Catalysts utilized in the processes of the invention can include a transition metal containing compound, the metal being selected from Group V, Group VI, and Group VIII of the Periodic Table, and mixtures of these metals.