Volatile organic compounds (VOCs) in cooking oil fumes need to be efficiently removed due to the significant damage they cause to the environment and human health. This review discusses the emission characteristics, which are influenced by different cooking temperatures, cooking oils, and cuisines. Then, various cooking oil fume purification methods are mainly classified into physical capture, chemical decomposition, and combination methods. VOCs removal rate, system operability, secondary pollution, application area, and cost are compared. The catalytic combustion method was found to have the advantages of high VOC removal efficiency, environmental protection, and low cost. Therefore, the last part of this review focuses on the research progress of the catalytic combustion method and summarizes its mechanisms and catalysts. The Marse-van Krevelen (MVK), Langmuir-Hinshelwood (L-H), and Eley-Rideal (E-R) mechanisms are analyzed. Noble metal and non-noble metal catalysts are commonly used. The former showed excellent activity at low temperatures due to its strong adsorption and electron transfer abilities, but the high price limits its application. The transition metals primarily comprise the latter, including single metal and composite metal catalysts. Compared to single metal catalysts, the interaction between metals in composite metal catalysts can further enhance the catalytic performance.