By mimicking Nature, we can design and synthesize inorganic smart materials that are reactive to biological tissues. These smart materials can be utilized to design innovative thirdgeneration biomaterials, which are able to not only optimize their interaction with biological tissues and environment, but also mimic biogenic materials in their functionalities. The biomedical applications involve increasing the biomimetic levels from chemical composition, structural organization, morphology, mechanical behavior, nanostructure, and bulk and surface chemical-physical properties until the surface becomes bioreactive and stimulates cellular materials. The chemical-physical characteristics of biogenic hydroxyapatites from bone and tooth have been described, in order to point out the elective sides, which are important to reproduce the design of a new biomimetic synthetic hydroxyapatite. This review outlines the evolving applications of biomimetic synthetic calcium phosphates, details the main characteristics of bone and tooth, where the calcium phosphates are present, and discusses the chemical-physical characteristics of biomimetic calcium phosphates, methods of synthesizing them, and some of their biomedical applications.