Trace elemental mercury in flue gas of coal burning is one of the main atmospheric mercury emission sources in China. How to achieve efficient removal of elemental mercury in flue gas of coal burning is the focus of attention and research in China. Previously, scholars have conducted in-depth studies on the effectiveness and reaction mechanism of existing devices for co-dehumidification, catalyst oxidation, plasma oxidation, photocatalytic oxidation, free radical oxidation and adsorbent in terms of different reaction components, reaction concentrations, reaction temperatures and reaction air velocities. However, the practical application of elemental mercury still faces many bottlenecks due to the obstacles of competition caused by the competition of flue gas components of SO2 and H2O for active sites, low adsorption capacity and secondary waste pollution. This study systematically introduced the different ways and characteristics of elemental mercury capture at present and focused on analyzing the influence of different experimental conditions on the application of catalysts and adsorbents in mercury removal. The progress of the present stage of mercury removal was summarized, including how to overcome the mercury removal toxicity of H2O and SO2, select the appropriate reaction temperature, obtain stable mercury removal compounds, explore safe and simple sample preparation methods, and realize the directional loading of functional groups at active sites. The results show that the loading of sulfur active sites can effectively resist the influence of SO2 in flue gas. Methyl groups and specific structures can make the adsorbent have high hydrophobic characteristics. Suitable pore structure and adsorbents with certain layer spacing can improve the performance of mercury removal by overcoming the limitation of the mass transfer diffusion step. The actual conditions in flue gas, such as flow field and physical-chemical reactions, affect the time evolution and internal evolution of fluid mass transfer to deviate from the standard, and influence the practical application of the adsorbent. The experimental effect analysis, kinetic analysis model and density functional theory reflect the influence of the limiting factors of elemental mercury removal, migration path and the influence of external reaction parameters and internal structure. The analysis of the adsorption configuration and migration paths of gaseous singlet mercury on defective and intact surfaces, for example, can reveal the adsorption process of singlet mercury. In terms of separation and regeneration, the actual spray application of the existing adsorbents, the influencing factors and the regeneration mode of the adsorbents were compared. It is found that the introduction of metals or metal-like oxides can improve the separation problem of adsorbents and the regeneration effect and the high regeneration temperature are the problems faced in the regeneration process. The adsorbent is generally regenerated by heat treatment. The regeneration temperature of heat treatment is 300-500 ℃, and the regeneration time is generally 30-180 min, which can achieve high mercury removal efficiency. The regeneration is realized by supplementing the corresponding active sites and functional groups. Finally, the bottleneck, challenge and optimization direction of catalysts and adsorbents were prospected, which can provide reference for the industrial application of elemental mercury control.