Biomineralization is a dynamic, complex, lifelong process by which living organisms control precipitations of inorganic nanocrystals within organic matrices to form unique hybrid biological tissues, for example, enamel, dentin, cementum, and bone. Understanding the process of mineral deposition is important for the development of treatments for mineralization-related diseases and also for the innovation and development of scaffolds. This review provides a thorough overview of the up-to-date information on the theories describing the possible mechanisms and the factors implicated as agonists and antagonists of mineralization. Then, the role of calcium and phosphate ions in the maintenance of teeth and bone health is described. Throughout the life, teeth and bone are at risk of demineralization, with particular emphasis on teeth, due to their anatomical arrangement and location. Teeth are exposed to food, drink, and the microbiota of the mouth; therefore, they have developed a high resistance to localized demineralization that is unmatched by bone. The mechanisms by which demineralization–remineralization process occurs in both teeth and bone and the new therapies/technologies that reverse demineralization or boost remineralization are also scrupulously discussed. Technologies discussed include composites with nano- and micron-sized inorganic minerals that can mimic mechanical properties of the tooth and bone in addition to promoting more natural repair of surrounding tissues. Turning these new technologies to products and practices would improve health care worldwide.