Biostable polyurethanes (PURs) have been incorporated in biomedical devices since the 1960s. The mechanisms of degradation and compositions with improved in vivo biostability have been investigated extensively. In recent years, biodegradable PURs have been investigated for applications in regenerative medicine. In contrast to the biostable implants, these biomaterials are designed to undergo controlled degradation in vivo and promote ingrowth of new tissue. Tissue-engineered scaffolds have been fabricated from biodegradable PURs using a variety of techniques, including thermally induced phase separation, salt leaching, wet spinning, electrospinning, and carbon dioxide foaming. These materials have been reported to support the ingrowth of cells and tissue in vitro and in vivo, and undergo controlled degradation to noncytotoxic decomposition products. Due to their tunable biological, mechanical, and physicochemical properties, biodegradable PURs present compelling future opportunities as scaffolds for regeneration of tissue. This review article summarizes recent advances made in the synthesis of biodegradable PURs and the application of these materials as scaffolds for regenerative medicine.