Cryogels obtained by the cryotropic gelation process are macroporous hydrogels with a well-developed system of interconnected pores and shape memory. There have been significant recent advancements in our understanding of the cryotropic gelation process, and in the relationship between components, their structure and the application of the cryogels obtained. As cryogels are one of the most promising hydrogel-based biomaterials, and this field has been advancing rapidly, this review focuses on the design of biodegradable cryogels as advanced biomaterials for drug delivery and tissue engineering. The selection of a biodegradable polymer is key to the development of modern biomaterials that mimic the biological environment and the properties of artificial tissue, and are at the same time capable of being safely degraded/metabolized without any side effects. The range of biodegradable polymers utilized for cryogel formation is overviewed, including biopolymers, synthetic polymers, polymer blends, and composites. The paper discusses a cryotropic gelation method as a tool for synthesis of hydrogel materials with large, interconnected pores and mechanical, physical, chemical and biological properties, adapted for targeted biomedical applications. The effect of the composition, cross-linker, freezing conditions, and the nature of the polymer on the morphology, mechanical properties and biodegradation of cryogels is discussed. The biodegradation of cryogels and its dependence on their production and composition is overviewed. Selected representative biomedical applications demonstrate how cryogel-based materials have been used in drug delivery, tissue engineering, regenerative medicine, cancer research, and sensing.