The rich structures and hierarchical organizations in nature provide many sources of inspiration for advanced material designs. We wish to recapitulate properties such as high mechanical strength, colour-changing ability, autonomous healing and antimicrobial efficacy in next-generation synthetic materials. Common in nature are non-covalent interactions such as hydrogen bonding, ionic interactions and hydrophobic effects, which are all useful motifs in tailor-made materials. Among these are biobased components, which are ubiquitously conceptualized in the space of recently developed bioinspired and biomimetic materials. In this regard, sustainable organic polymer chemistry enables us to tune the properties and functions of such materials that are essential for daily life. In this Review, we discuss recent progress in bioinspired and biomimetic polymers and provide insights into biobased materials through the evolution of chemical approaches, including networking/crosslinking, dynamic interactions and self-assembly. We focus on advances in biobased materials; namely polymeric mimics of resilin and spider silk, mechanically and optically adaptive materials, self-healing elastomers and hydrogels, and antimicrobial polymers.