Sustainable technologies applied to energy-related applications should develop a pivotal role in the next decades. In particular, carbon dioxide capture from flue gases emitted by fossil-fueled power plants should play a pivotal role in controlling and reducing the greenhouse effect. Therefore, the development of new materials for carbon capture purposes has merged as central research line, for which many alternatives have been proposed. Ionic liquids (ILs) have emerged as one of the most promising choices for carbon capture, but in spite of their promising properties, some serious drawbacks have also appeared. Deep eutectic solvents (DESs) have recently been considered as alternatives to ILs that maintain most of their relevant properties, such as task-specific character, and at the same time avoid some of their problems, mainly from economic and environmental viewpoints. DES production from low-cost and natural sources, together with their almost null toxicity and total biodegradability, makes these solvents a suitable platform for developing gas separation agents within the green chemistry framework. Therefore, because of the promising characteristics of DESs as CO2 absorbents and in general as gas separating agents, the state of the art on physicochemical properties of DESs in relationship to their influence on gas separation mechanisms and on the studies of gas solubility in DESs are discussed. The objective of this review work is to analyze the current knowledge on gas separation using DESs, comparing the capturing abilities and properties of DESs with those of ILs, inferring the weaknesses and strengths of DESs, and proposing future research directions on this subject.