A shift to a bioeconomy development model has been evolving, conducting the scientific community to investigate new ways of producing chemicals, materials and fuels from renewable resources, i.e., biomass. Specifically, technologies that provide high performance and maximal use of biomass feedstocks into commodities with reduced environmental impact have been highly pursued. A key example comprises the extraction and/or dissolution of polysaccharides, one of the most abundant fractions of biomass, which still need to be improved regarding these processes’ efficiency and selectivity parameters. In this context, the use of alternative solvents and the application of less energy-intensive processes in the extraction of polysaccharides might play an important role to reach higher efficiency and sustainability in biomass valorization. This review debates the latest achievements in sustainable processes for the extraction of polysaccharides from a myriad of biomass resources, including lignocellulosic materials and food residues. Particularly, the ability of ionic liquids (ILs) and deep eutectic solvents (DESs) to dissolve and extract the most abundant polysaccharides from natural sources, namely cellulose, chitin, starch, hemicelluloses and pectins, is scrutinized and the efficiencies between solvents are compared. The interaction mechanisms between solvent and polysaccharide are described, paving the way for the design of selective extraction processes. A detailed discussion of the work developed for each polysaccharide as well as the innovation degree and the development stage of dissolution and extraction technologies is presented. Their advantages and disadvantages are also identified, and possible synergies by integrating microwave- and ultrasound-assisted extraction (MAE and UAE) or a combination of both (UMAE) are briefly described. Overall, this review provides key information towards the design of more efficient, selective and sustainable extraction and dissolution processes of polysaccharides from biomass.