Polydepsipeptides - alternating copolymers of an alpha-amino acid and an alpha-hydroxy acid - are a group of biodegradable polymers. Versatile polydepsipeptides with or without pendant functional groups, as well as various polymer architectures, for example, providing alternative, random, diblock, triblock, multiblock or graft sequence structures, can be synthesized via ring-opening copolymerization of various morpholine-2,5-dione derivatives. They are potential candidates for a wide range of biomedical applications. Polydepsipeptides are described in this review from the aspect of materials science, especially as biomaterials. We mainly focus on various techniques developed to synthesize polydepsipeptides and their copolymers, biodegradation behaviors, shape-memory properties and possible biomedical applications.