Mineralization is a common strategy found in structural biological materials to achieve the high stiffness and hardness required for skeletal support, protection or predation. While high mineral content generally also leads to brittleness, natural materials such as bone, mollusk shells or glass sponge achieve extremely high toughness relative to their constituents. Toughness is generated by various processes including crack deflection, crack bridging or energy dissipation, and all these processes are controlled by the weaker interfaces that these materials contain. Here I will discuss some key mechanisms at the interfaces including adhesive vs. cohesive fracture, elastomeric deformation and entropy, cavitation and formation of ligaments, crack deflection and also proteins with sacrificial bonds, Velcro-like mechanisms mediated by hydrogen bonds. I will also discuss how we are duplicating some of these interface mechanisms using friction, highly viscous polymers and ionomers to produce new bio-inspired engineering materials with outstanding properties.