In contrast to synthetic materials, evolutionary developments in biology have resulted in materials with remarkable structural properties, made out of relatively weak constituents, arranged in complex hierarchical patterns. For instance, nacre from seashells is primarily made of a fragile ceramic, yet it exhibits superior levels of strength and toughness. Structural features leading to this performance consist of a microstructure organized in a hierarchical fashion, and the addition of a small volume fraction of biopolymers. A key to this mechanical performance is the cohesion and sliding of wavy ceramic tablets. Another example is bone, a structural biological material made of a collagen protein phase and nanoscopic mineral platelets, reaching high levels of toughness and strength per weight. The design and fabrication of de novo synthetic materials that aim to utilize the deformation and hardening mechanism of biological materials such as bone or nacre is an active area of research in mechanics of materials. In this review, our current knowledge on microstructure and mechanics of nacre and bone are described, and a review of the fabrication of nacre-inspired artificial and related materials is presented. Both experimental and simulation approaches are discussed, along with specific examples that illustrate the various approaches. We conclude with a broader discussion of the interplay of size effects and hierarchies in defining mechanical properties of biological materials.