Calcium phosphate apatites offer outstanding biological adaptability that can be attributed to their specific physico-chemical and structural properties. The aim of this review is to summarize and discuss the specific characteristics of calcium phosphate apatite biominerals in vertebrate hard tissues (bone, dentine and enamel). Firstly, the structural, elemental and chemical compositions of apatite biominerals will be summarized, followed by the presentation of the actual conception of the fine structure of synthetic and biological apatites, which is essentially based on the existence of a hydrated layer at the surface of the nanocrystals. The conditions of the formation of these biominerals and the hypothesis of the existence of apatite precursors will be discussed. Then, we will examine the evolution of apatite biominerals, especially during bone and enamel aging and also focus on the adaptability of apatite biominerals to the biological function of their related hard tissues. Finally, the diagenetic evolution of apatite fossils will be analyzed.