This review will discuss, under the Circular Economy and Biorefinery concepts, the performance of the alternative solvents in the downstream process to recover natural pigments in a more sustainable way. Conventionally, pigments marketed on an industrial scale are produced through chemical synthesis by using petroleum derivatives as the main raw material. Also, the current production chain of the synthetic dyes is linear, with no solvent recycling and waste generation. Thus, the most promising processes of extraction and purification of natural pigments and strategies on the polishing of the solvents are here reviewed. In this review, the use of alternative solvents, namely, ionic liquids, eutectic solvents, aqueous solutions of surfactants, and edible oils, for recovering natural pigments was reviewed. Works discussing higher extraction yields and selectivity, while maintaining the stability of the target pigments, were reported. Also, a panorama between Sustainability and Circular Economy prospection was discussed for better comprehension of the main advances in the field. Behind the analysis of the works published so far on the theme, the most important lacunas to overcome in the next years on the field were pointed out and discussed. Also, the future trends and new perspectives to achieve the economic viability and sustainability of the processes using alternative solvents will be scrutinized.