Organ repair, regeneration, and transplantation are constantly in demand due to various acute, chronic, congenital, and infectious diseases. Apart from traditional remedies, tissue engineering (TE) is among the most effective methods for the repair of damaged tissues via merging the cells, growth factors, and scaffolds. With regards to TE scaffold fabrication technology, polyurethane (PU), a high-performance medical grade synthetic polymer and bioactive material has gained significant attention. PU possesses exclusive biocompatibility, biodegradability, and modifiable chemical, mechanical and thermal properties, owing to its unique structure-properties relationship. During the past few decades, PU TE scaffold bioactive properties have been incorporated or enhanced with biodegradable, electroactive, surface-functionalised, ayurvedic products, ceramics, glass, growth factors, metals, and natural polymers, resulting in the formation of modified polyurethanes (MPUs). This review focuses on the recent advances of PU/MPU scaffolds, especially on the biomedical applications in soft and hard tissue engineering and regenerative medicine. The scientific issues with regards to the PU/MPU scaffolds, such as biodegradation, electroactivity, surface functionalisation, and incorporation of active moieties are also highlighted along with some suggestions for future work.