Bioinspired polymers have emerged as promising materials for regenerative medicine (RM) owing to their unique properties. Polymers, which can be natural, synthetic, or hybrid, have been created and applied in numerous applications such as tissue engineering (TE), wound healing, drug delivery, and the creation of artificial organs. The biocompatibility and biodegradability of these polymers have been extensively studied to ensure polymer safety and effectiveness in-vivo. Bioinspired polymers including polydopamine (PDA), spider silk, nacre-like polymer, ulvan, polypeptoids, gecko-inspired polymers, shark skin, and elastin-like polymers (ELPs) have also shown potential in personalized medicine and enhancing mechanical properties, and mimicking the extracellular matrix (ECM). An overview of the many bioinspired polymer types utilized in RM, together with information on their uses, characteristics, and potential future research and development directions, are provided. The potential impact of bioinspired polymers in RM is significant, and further research is needed to fully realize their potential in improving human health.