Vertebrate mineralized tissues, present in bones, teeth and scales, have complex 3D hierarchical structures. As more of these tissues are characterized in 3D using mainly FIB SEM at a resolution that reveals the mineralized collagen fibrils and their organization into collagen fibril bundles, highly complex and diverse structures are being revealed. In this perspective we propose an approach to analyzing these tissues based on the presence of modular structures: material textures, pore shapes and sizes, as well as extents of mineralization. This modular approach is complimentary to the widely used hierarchical approach for describing these mineralized tissues. We present a series of case studies that show how some of the same structural modules can be found in different mineralized tissues, including in bone, dentin and scales. The organizations in 3D of the various structural modules in different tissues may differ. This approach facilitates the framing of basic questions such as: are the spatial relations between modular structures the same or similar in different mineralized tissues? Do tissues with similar sets of modules carry out similar functions or can similar functions be carried out using a different set of modular structures? Do mineralized tissues with similar sets of modules have a common developmental or evolutionary pathway? 3D organization studies of diverse vertebrate mineralized tissues are revealing detailed, but often confusing details about the material textures, the arrangements of pores and differences in the extent of mineralization within a tissue. The widely used hierarchical scheme for describing such organizations does not adequately provide a basis for comparing these tissues, or addressing issues such as structural components thought to be characteristic of bone, being present in dermal tissues and so on. The classification scheme we present is based on identifying structural components within a tissue that can then be systematically compared to other vertebrate mineralized tissues. We anticipate that this classification approach will provide insights into structure-function relations, as well as the evolution of these tissues. Display omitted