Hydrotreating catalysis refers to a various hydrogenation which saturate an unsaturated hydrocarbon, together with removing heteroatoms such as sulfur, nitrogen, oxygen, and trace metals from different petroleum streams in a refinery. Most refineries include at least three hydrotreating units for upgrading naphtha, middle distillates, gas oils, intermediate process streams, and/or residue. Among them, hydrotreating catalysis for residue are the core of the process, because of its complexity. This article reviews recent progress in tackling the issues found in the upgrading residues by hydrotreating, focusing on the chemistry of hydrodemetallization (HDM) and hydrodesulfurization (HDS). We also discuss the composition and functions of hydrotreating catalysts, and we highlight areas for further improvement.