Under eons of evolutionary and environmental pressure, biological systems have developed strong and lightweight peptide-based polymeric materials by using the 20 naturally occurring amino acids as principal monomeric units. These materials outperform their man-made counterparts in the following ways: 1) multifunctionality/tunability, 2) adaptability/stimuli-responsiveness, 3) synthesis and processing under ambient and aqueous conditions, and 4) recyclability and biodegradability. The universal design strategy that affords these advanced properties involves “bottom-up” synthesis and modular, hierarchical organization both within and across multiple length-scales. The field of “biomimicry”—elucidating and co-opting nature’s basic material design principles and molecular building blocks—is rapidly evolving. This Review describes what has been discovered about the structure and molecular mechanisms of natural polymeric materials, as well as the progress towards synthetic “mimics” of these remarkable systems.