Deep eutectic solvents are promising alternative media for more sustainable chemistry and chemical engineering. The way they dissolve gases provides valuable information about solvation mechanisms but also points the way to new applications of these interesting liquid mixtures. Here we review the solubility of 10 permanent gases in 87 deep eutectic solvents: carbon dioxide (CO2), carbon monoxide (CO), nitric oxide (NO), nitrogen dioxide (NO2), hydrogen (H2), hydrogen sulfide (H2S), sulfur dioxide (SO2), nitrogen (N2), ammonia (NH3), and methane (CH4). The gas solubility studies were performed using either saturation or gravimetric techniques. Carbon dioxide is the most studied gas so far, followed by SO2 and NH3. Although for some gases the absorption process is only physical, e.g., N2, CO, and CH4, for others it was reported to be both physical and chemical, e.g., SO2, NO, and CO2. The solubility of the most commonly studied gases varies in the order SO2 > NO > CO2 > H2S, the larger absorption for SO2 being reported for the common choline chloride:urea mixtures with Henry’s law constant lower than 0.18 bar at 293 K. The larger solubilities for NO, H2S, and CO2 were measured for mixtures based in tetraalkylphosphonium salts, with Henry’s law constants typically below 0.20 bar at 303 K. Eutectic mixtures containing amines are also reported as excellent absorbers of CO2, this behavior being probably explained by a chemical reaction between the gas and these components of the eutectic mixture.