Polymeric materials are widely used in every human endeavor (bottles, clothes, containers, toys, tools, etc.) due to their unique properties of chemical and mechanical resistance. They are, however, almost non-biodegradable, and their chemical recycling into monomers is difficult and costly, thereby allowing their accumulation into the environment. This review highlights recent advances in the use of deep eutectic solvents (DESs) as catalysts and/or green solvents in plastics degradation, with the aim of designing greener processes for polymers’ chemical recycling, by reusing their monomers. These greener processes, in combination with other catalytic approaches, are aimed at introducing plastics as feedstock into the synthesis of other materials, according to the circular economy principles.