Up to now, many kinds of deep eutectic solvents (DESs) were investigated for the capture of acidic gases from flue gases. In this review, non-functionalized and functionalized DESs, including binary and ternary DESs, for SO2, CO2 and NO capture, are summarized based on the mechanism of absorption, physical interaction or chemical reaction. New strategies for improving the absorption capacity are introduced in this review. For example, a third component can be introduced to form a ternary DES to suppress the increase in viscosity and improve the CO2 absorption capacity. DESs, synthesized with halogen salt hydrogen bond acceptors (HBAs) and functionalized hydrogen bond donors (HBDs), can be used for the absorption of SO2 and NO with high absorption capacities and low viscosities after absorption, due to physicochemical interaction between gases and DESs. Emphasis is given to introducing the absorption capacities of acidic gases in these DESs, the mechanism of the absorption, and the ways to enhance the absorption capacity.