Biological composites have evolved elaborate hierarchical structures to achieve outstanding mechanical properties using weak but readily available building blocks. Combining the underlying design principles of such biological materials with the rich chemistry accessible in synthetic systems may enable the creation of artificial composites with unprecedented properties and functionalities. This bioinspired approach requires identification, understanding, and quantification of natural design principles and their replication in synthetic materials, taking into account the intrinsic properties of the stronger artificial building blocks and the boundary conditions of engineering applications. In this progress report, the scientific and technological questions that have to be addressed to achieve this goal are highlighted, and examples of recent research efforts to tackle them are presented. These include the local characterization of the heterogeneous architecture of biological materials, the investigation of structure–function relationships to help unveil natural design principles, and the development of synthetic processing routes that can potentially be used to implement some of these principles in synthetic materials. The importance of replicating the design principles of biological materials rather than their structure per se is highlighted, and possible directions for further progress in this fascinating, interdisciplinary field are discussed.