Molecular self-assembly has paved the way to create novel, supramolecular, functional biomaterials. Peptide-based biomaterials are gaining interest as a result of their programmability, biodegradability, and bioresorbability. Further, unlike polymeric materials, peptides can be made monodisperse with precise control over sequence, chain length, and stereochemistry. Peptide-based viscoelastic matrices have been designed and characterized for various biomedical applications, such as tissue engineering scaffolds or drug delivery vehicles. The 'holy grail' in designing an ideal tissue engineering scaffold lies in mimicking the cues of the tissue's natural extracellular matrix (ECM). Some of the key elements of ECM that are incorporated into these peptide scaffolds include cell-adhesive and protease-sensitive sequences for enhanced cell-cell and cell-biomaterial interactions. Peptide-based viscoelastic matrices can also be engineered with drug carrying protease-sensitive sequences for controlled and site-specific drug delivery. Molecular-level engineering of simple oligopeptide modules can be used to control the position and density of the bio-mimetic functionalities in the supramolecular structures, which demonstrates the power of the 'bottom-up' approach in self-assembly.