Natural structural materials are built at ambient temperature from a fairly limited selection of components. They usually comprise hard and soft phases arranged in complex hierarchical architectures, with characteristic dimensions spanning from the nanoscale to the macroscale. The resulting materials are lightweight and often display unique combinations of strength and toughness, but have proven difficult to mimic synthetically. Here, we review the common design motifs of a range of natural structural materials, and discuss the difficulties associated with the design and fabrication of synthetic structures that mimic the structural and mechanical characteristics of their natural counterparts