As a carbon capture technology in combustion process， oxy⁃fuel combustion can achieve a high concentration of CO2 in flue gas. Before sequestering and utilizing CO2， the CO2⁃rich flue gas needs to be purified， dried and liquefied in a CO2 compression and purification system for ease of transportation and cost reduc⁃ tion. Current studies showed that the CO2 compression and purification system could achieve the combined removal of SOx， NOx and Hg， dry dehydration， separation of O2， N2 and other inert gases， and thus liquefy and purify CO2 gas under high pressure and low temperature. Based on the oxy⁃fuel combustion carbon capture technology， the combined removal of pollutants by sour compression in CO2 compression and purification system was introduced， and the reaction mechanism and interaction mechanism of synergistic removal of SOx ， NOx and Hg in the sour compression process were discussed. Several methods of dehydration and drying of carbon dioxide were briefly recommended， and a molecular sieve dehydration technology was explored. The main methods of high concentration CO2 liquefaction purification technology and the way of obtaining low temperature cold energy required by the CO2 liq⁃ uefaction purification system were compared and analyzed. The pilot scale and demonstration application of CO2 com⁃ pression purification technology for oxy⁃fuel flue gas at home and abroad were reviewed and the future development di⁃ rection was pointed out. The demonstration and application of the combined removal technology of acid compression pollutants lags behind the CO2 liquefaction and purification technology in China. It is indispensable to clarify the spe⁃ cific mechanism of combined removal of acid compression pollutants and the impact of operating parameters， and carry out the demonstration and application study of simultaneous removal of SO2， NOx and Hg in China. The current pilot scale demonstration project is not sufficient enough to study the operation characteristics of each unit of the CO2 com⁃ pression and purification system. Therefore， it is necessary to further develop the process and improve the system inte⁃ gration scheme， conduct the integration study of the one⁃million⁃ton CO2 compression and purification system scheme， and promote the large⁃scale industrial application of CO2 compression and purification technology.