Extracellular matrices (ECMs) are challenging design targets for materials synthesis because they serve multiple biological roles, and they are composed of multiple molecular constituents. In addition, their composition and activities are dynamic and variable between tissues, and they are difficult to study mechanistically in physiological contexts. Nevertheless, the design of synthetic ECMs is a central consideration in applications such as regenerative medicine and 3D cell culture. In order to produce synthetic matrices having both multi-component construction and high levels of compositional definition, strategies based on molecular self-assembly are receiving increasing interest. These approaches are described in this tutorial review and compared with the structures and processes in native ECMs that serve as their inspiration.