This paper is a critical and thorough (but not exhaustive) review of the literature of catalytic hydroprocessing reactions. It includes data chracterizing thermodynamics, reactivities, reaction networks, and kinetics of hydrogenation of aromatic hydrocarbons, hydrodesulfurization, hydrodenitrogenation, and hydrodeoxygenation. The subject is organized by reaction type, and there are separate sections on competitive reaction and inhibition effects. The results summarized are judged to be the most reliable and useful available to guide process modeling for hydroprocessing of heavy fossil fuels. The review is designed for use as a reference; most of the quantitative results are summarized in tables and figures, and a table of contents and a chart with names and structures of the organic compounds are also included.