This brief review focuses on the evolving concepts related to the kinetic modeling of catalytic hydrogenation systems involving organic compounds of large molecular size. After a short paragraph introducing the scope of the article, different mathematical approaches are reviewed from a Chemical Reaction Engineering viewpoint. Their chronological development is described, going from the early simple LHHW model to recent advanced models based on the concept of multicentered and semicompetitive adsorption. First, the review presents and critically analyzes the simplest mathematical attempts to deal with the classical kinetic models based upon extreme adsorption regimes, i.e., competitive and non-competitive adsorption between hydrogen and organic molecules. Then, it discusses progressive attempts based on more rigorous frameworks for conciliating the understanding of finite differences in the molecular size of species, admitting a distinction between occupied-sites and covered-sites by the large molecules of organic species. Accordingly, the concepts of multicentered and semi-competitive adsorption are brought on the scene, and recent proposals are analyzed in detail to link the two seemingly separate kinetic models describing the extreme modes of competitive and non-competitive adsorption. The additional indication of the number of surface sites that would likely be covered by organic molecules appears to be the most fascinating result of these advanced approaches. Finally, the review highlights the need for examining the robustness of these recent approaches.