This paper is a selective review on design approaches and associated catalysis and chemistry for deep desulfurization and deep dearomatization (hydrogenation) of hydrocarbon fuels, particularly diesel fuels. The challenge for deep desulfurization of diesel fuels is the difficulty of removing the refractory sulfur compounds, particularly 4,6-dimethyldibenzothiophene, with conventional hydrodesulfurization processes. The problem is exacerbated by the inhibiting effect of polyaromatics and nitrogen compounds, which exist in some diesel blend stocks on deep HDS. With the new Environmental Protection Agency (EPA) Tier H regulations to cut the diesel sulfur from current 500 ppmw down to 15 ppmw by June 2006, refineries are facing major challenges to meet the fuel sulfur specification along with the required reduction of aromatics contents. The principles and problems for the existing hydrodesulfurization processes, and the concepts, advantages and disadvantages of various new approaches will be discussed. Specifically, the following new design approaches for sulfur removal will be discussed: (1) novel catalysts for ultra-deep hydrodesulfurization under conventional HDS process conditions; (2) new design concept for sulfur-tolerant noble metal catalysts for low-temperature hydrogenation; (3) new desulfurization process by sulfur adsorption and capture under H-2; (4) new desulfurization process by selective adsorption at ambient temperature without H-2 and a related integrated process concept; (5) oxidative desulfurization in liquid-phase; and (6) biodesulfurization.