Protein- and peptide-based structural biopolymers are abundant building blocks of biological systems. Either in their natural forms, such as collagen, silk, and fibronectin, or as related synthetic materials, they can be used in various technologies. An emerging area is that of biomimetic materials inspired by protein-based biopolymers, which are made up of small molecules rather than macromolecules and can therefore be described as supramolecular polymers. These materials are very useful in biomedical applications because of their ability to imitate the extracellular matrix in both architecture and the capacity to signal cells. This article describes important features of the natural extracellular matrix and highlights how these features are being incorporated into biomaterials composed of biopolymers and supramolecular polymers. We particularly focus on the structures, properties, and functions of collagen, fibronectin, and silk, and the supramolecular polymers inspired by them as biomaterials for regenerative medicine.