Shape-memory polymers (SMPs) represent an emerging  class of smart materials capable of undergoing programmed  deformations and returning to their original shape upon exposure to external stimuli such as temperature, pH, light, or  magnetic and electric fields. Among them, shape-memory  polyurethanes (SMPUs) have attracted particular attention  due to their segmented structure, tunable thermal and mechanical properties, and, in some cases, biocompatibility.  Their versatility enables not only shape recovery but sometimes also biodegradation in physiological environments,  which significantly broadens their biomedical applicability.  This review provides a comprehensive overview of the  fundamental mechanisms behind the shape-memory effect, including the role of hard and soft segments, transition  temperatures, and the influence of structural modifications.  Special focus is given to the comparison between SMPs  and shape-memory alloys (SMAs), highlighting advantages  such as lower density, greater deformability, and biodegradability of some of the SMPs. Current biomedical applications of SMPs include vascular stents, drug delivery  systems, sutures, scaffolds for tissue engineering, wound  dressings, artificial muscles, and orthodontic devices. Additionally, porous polyurethane foams and biodegradable  films offer promising solutions in minimally invasive surgery  and regenerative medicine. Perspectives for future development emphasize improving long-term stability and degradation control, ensuring non-toxic by-products, and scaling  up production for clinical applications. The integration of  SMPs with additive manufacturing techniques, nanofillers,  and multifunctional stimuli-responsiveness is expected to  significantly expand their role in next-generation medical  devices. Collectively, SMPs stand out as one of the most  promising groups of materials at the interface of polymer  science and biomedicine.