From an engineering perspective, skeletal tissues are remarkable structures because they are lightweight, stiff and tough, yet produced at ambient conditions. The biomechanical success of skeletal tissues is largely attributable to the process of biomineralization — a tightly regulated, cell-driven formation of billions of inorganic nanocrystals formed from ions found abundantly in body fluids. In this Review, we discuss nature's strategies to produce and sustain appropriate biomechanical properties in mineralizing (by the promotion of mineralization) and non-mineralizing (by the inhibition of mineralization) tissues. We review how perturbations of biomineralization are controlled over a continuum that spans from the desirable (or defective in disease) mineralization of the skeleton to pathological cardiovascular mineralization, and to mineralization of bioengineered constructs. A materials science vision of mineralization is presented with an emphasis on the micro- and nanostructure of mineralized tissues recently revealed by state-of-the-art analytical methods, and on how biomineralization-inspired designs are influencing the field of synthetic materials.