Poly(ethylene glycol)-based hydrogels have long proved to be promising materials for various biomedical technologies. This review considers systems based on the most common and studied copolymers of poly(ethylene glycol) and biodegradable polyesters of lactide and glycolide. Traditional and modern approaches to the synthesis of the copolymers and the production of hydrogels have been considered, the studies of the structure and properties of the materials have been analyzed, and the main directions of the application of these products in practice have been described.