An emerging approach for design of dynamic materials involves mimicking natural systems, which are adept at changing their structure and function in response to their environment. Biological systems possess a diverse range of dynamic mechanisms, including competitive ligand–protein binding, enzyme-catalyzed remodeling, and allosteric protein conformational changes. These dynamic mechanisms are now being exploited by materials scientists and engineers to design “bioinspired” synthetic materials that undergo responsive assembly and disassembly as well as dynamic volume and shape changes. The purpose of this review is to describe recent progress in design and development of bioinspired dynamic materials, with a particular emphasis on hydrogel networks. We specifically focus on emerging approaches that use biological phenomena as an inspiration for design of materials.