Graft copolymers of polysaccharides with acrylic monomers combine biodegradability, biocompatibility, the environmental friendliness of natural polymers and the increased thermal stability, chemical and mechanical resistance of synthetic polymers. This paper describes our search and analysis of the literature in English for 2002–2022 devoted to the graft polymerization of acrylamide, acrylic acid and 2-acrylamido2-methylpropanesulfonic acid onto xanthan and glucomannan macromolecular chains.