The environmental regulation pressure is being increased to reduce precursors of pollution contaminants (sulfur, nitrogen, and aromatics) in fuels to lower levels. There are various processes to upgrade heavy and extra-heavy crude oils, such as solvent deasphalting, thermal conversion, catalytic conversion, distillation, and hydroprocessing. Hydroprocessing not only upgrades the crude oil but also produces synthetic crude oil that has a lower impurities content and a higher liquid yield of products. The fuels upgrading currently is achieved in refinery hydroprocessing units using different new-generation catalysts, along with several modifications of process conditions such as multistage reactors, type of catalyst loading, and reactor internals. However, it has been widely recognized that, for deep removal of these contaminants by hydroprocessing, research must be more oriented to the catalyst developments, rather than the process conditions. Actual commercial catalysts are based on well-known and studied active metals (CoMo, NiMo) and support (Al2O3). In addition, extensive research work has been performed with other supports (Al2O3-TiO2, Al2O3-ZrO2, etc.). Nevertheless, other promising acidic materials, such as zeolites, have received relatively less attention, and experimental reports on their use as part of the heavy oil hydroprocessing catalyst support are scarce in the literature. The objective of this contribution is then to discuss the use of acidic and/or basic materials as a support for the hydroprocessing catalyst, specifically for their possible application for the hydroprocessing of heavy oils, in cases where the desired product selectivity is toward gasoline and middle distillates.