The inorganic part of hard tissues (bones and teeth) of mammals consists of calcium phosphate, mainly of apatitic structure. Similarly, most undesired calcifications (i.e. those appearing as a result of various diseases) of mammals also contain calcium phosphate. For example, atherosclerosis results in blood-vessel blockage caused by a solid composite of cholesterol with calcium phosphate. Dental caries result in a replacement of less soluble and hard apatite by more soluble and softer calcium hydrogenphosphates. Osteoporosis is a demineralization of bone. Therefore, from a chemical point of view, processes of normal (bone and teeth formation and growth) and pathological (atherosclerosis and dental calculus) calcifications are just an in vivo crystallization of calcium phosphate. Similarly, dental caries and osteoporosis can be considered to be in vivo dissolution of calcium phosphates. On the other hand, because of the chemical similarity with biological calcified tissues, all calcium phosphates are remarkably biocompatible. This property is widely used in medicine for biomaterials that are either entirely made of or coated with calcium phosphate. For example, self-setting bone cements made of calcium phosphates are helpful in bone repair and titanium substitutes covered with a surface layer of calcium phosphates are used for hip-joint endoprostheses and tooth substitutes, to facilitate the growth of bone and thereby raise the mechanical stability. Calcium phosphates have a great biological and medical significance and in this review we give an overview of the current knowledge in this subject.