Shape memory materials have emerged as an important class of materials in medicine due to their ability to change shape in response to a specific stimulus, enabling the simplification of medical procedures, use of minimally invasive techniques, and access to new treatment modalities. Shape memory polymers, in particular, are well suited for such applications given their excellent shape memory performance, tunable materials properties, minimal toxicity, and potential for biodegradation and resorption. This review provides an overview of biodegradable shape memory polymers that have been used in medical applications. The majority of biodegradable shape memory polymers are based on thermally responsive polyesters or polymers that contain hydrolyzable ester linkages. These materials have been targeted for use in applications pertaining to embolization, drug delivery, stents, tissue engineering, and wound closure. The development of biodegradable shape memory polymers with unique properties or responsiveness to novel stimuli has the potential to facilitate the optimization and development of new medical applications.