Billions of years of evolution have produced extremely efficient natural materials, which are increasingly becoming a source of inspiration for engineers. Biomimetics—the science of imitating nature—is a growing multidisciplinary field which is now leading to the fabrication of novel materials with remarkable mechanical properties. This article discusses the mechanics of hard biological materials, and more specifically of nacre and bone. These high-performance natural composites are made up of relatively weak components (brittle minerals and soft proteins) arranged in intricate ways to achieve specific combinations of stiffness, strength and toughness (resistance to cracking). Determining which features control the performance of these materials is the first step in biomimetics. These ‘key features’ can then be implemented into artificial bio-inspired synthetic materials, using innovative techniques such as layer-by-layer assembly or ice-templated crystallization. The most promising approaches, however, are self-assembly and biomineralization because they will enable tight control of structures at the nanoscale. In this ‘bottom-up’ fabrication, also inspired from nature, molecular structures and crystals are assembled with a little or no external intervention. The resulting materials will offer new combinations of low weight, stiffness and toughness, with added functionalities such as self-healing. Only tight collaborations between engineers, chemists, materials scientists and biologists will make these ‘next-generation’ materials a reality.