It is undisputed that there is a paradigm shift in the global trend of crude oil towards being more sour and heavier than usual light sources. Consequently, the hydrotreating activity becomes a bottleneck with high content of S, N, metals and other impurities than expected. On the other hand, the price of petroleum products lately witnessed instability and fell to the lowest average price (<USD 20) in recent times. In the same vein, the regulation to control the emission of toxic compounds in the atmosphere become stricter as promulgated by various policymakers. In this sense, robust hydrotreating catalysts with characteristics efficient catalytic activity, selectivity and stability are highly desirable. Recently, different approaches have been used to improve and cushion the unprecedented effect emanated from economic, social and environmental challenges posed by heavy and sour crude sources, price instability of the refined products and regulation to lower the sulfur to minimum level or zero parts per millions (ppm). Importantly, the role of support in catalysis cannot be over emphasized, whilst the surface area and porosity, mechanical and thermal stability, dispersion of active metals, acidity/basicity have been greatly improved, the increased activity, stability and selectivity has been observed significantly. In this review, hybrid supports based on aluminosilicates (zeolitic types) and other notable supports from recent literatures were explored and discussed for Ni(Co)Mo(W) supported catalysts for hydrodesulfurization (HDS) activity of heavy organosulfur molecules. The emphasis on the hybrid supports’ varied characteristics for HDS of organosulfur molecules, where there are necessities for fast diffusion of reactants and products, better dispersion of MoS2 crystallites, high surface area and pore volume, and increased acidity of the catalysts are greatly emphasized. Furthermore, the progress made so far on different HDS active phases viz. noble metals, metal phosphides, intermetallic silicides, carbides and iron‐zinc are highlighted in this write‐up, irrespective of the support composition in the supported catalysts formulations. The need for application of predictive tools, like machine learning (ML) in the design and development of HDS catalysts, and performance evaluation of HDS activity towards achieving better catalytic operation was briefly highlighted. Finally, the review will serve as a summary of scientific efforts in this regards and bridge a gap for the newcomers to investigate the topic in a better way through proper selection and efficient catalysts design.