Biomedical polymers play a key role in preventing, diagnosing, and treating diseases, showcasing a wide range of applications. Their unique advantages, such as rich source, good biocompatibility, and excellent modifiability, make them ideal biomaterials for drug delivery, biomedical imaging, and tissue engineering. However, conventional biomedical polymers suffer from poor degradation in vivo, increasing the risks of bioaccumulation and potential toxicity. To address these issues, degradable biomedical polymers can serve as an alternative strategy in biomedicine. Degradable biomedical polymers can efficiently relieve bioaccumulation in vivo and effectively reduce patient burden in disease management. This review comprehensively introduces the classification and properties of biomedical polymers and the recent research progress of degradable biomedical polymers in various diseases. Through an in-depth analysis of their classification, properties, and applications, we aim to provide strong guidance for promoting basic research and clinical translation of degradable biomedical polymers.