Bone is a complex hierarchically structured family of materials that includes a network of cells and their interconnected cell processes. New insights into the 3-D structure of various bone materials (mainly rat and human lamellar bone and minipig fibrolamellar bone) were obtained using a focused ion beam electron microscope and the serial surface view method. These studies revealed the presence of two different materials, the major material being the well-known ordered arrays of mineralized collagen fibrils and associated macromolecules, and the minor component being a relatively disordered material composed of individual collagen fibrils with no preferred orientation, with crystals inside and possibly between fibrils, and extensive ground mass. Significantly, the canaliculi and their cell processes are confined within the disordered material. Here we present a new hierarchical scheme for several bone tissue types that incorporates these two materials. The new scheme updates the hierarchical scheme presented by Weiner and Wagner (1998). We discuss the structures at different hierarchical levels with the aim of obtaining further insights into structure–function-related questions, as well as defining some remaining unanswered questions.