Biomineralization can be considered as nature's strategy to produce and sustain biominerals, primarily via creation of hard tissues for protection and support. This review examines the biomineralization process within the hard tissues of the human body with special emphasis on the mechanisms and principles of bone and teeth mineralization. We describe the detailed role of proteins and inorganic ions in mediating the mineralization process. Furthermore, we highlight the various available models for studying bone physiology and mineralization starting from the historical static cell line-based methods to the most advanced 3D culture systems, elucidating the pros and cons of each one of these methods. With respect to the mineralization process in teeth, enamel and dentin mineralization is discussed in detail. The key role of intrinsically disordered proteins in modulating the process of mineralization in enamel and dentine is given attention. Finally, nanotechnological interventions in the area of bone and teeth mineralization, diseases and tissue regeneration is also discussed.