Amorphous calcium phosphates (ACPs) represent a unique class of biomedically relevant calcium orthophosphate salts, in which there are neither translational nor orientational long-range orders of the atomic positions. Nevertheless, the constancy in their chemical composition over a relatively wide range of preparation conditions suggests the presence of a well-defined local structural unit, presumably, with the structure of Ca9(PO4)6 – so-called Posner’s cluster. ACPs have variable chemical but rather identical glass-like physicochemical properties. Furthermore, all ACPs are thermodynamically unstable compounds and, unless stored in dry conditions or doped by stabilizers, spontaneously they tend to transform to crystalline calcium orthophosphates. Although some order within general disorder is the most distinguishing feature of ACPs, the solution instability of ACPs and their easy transformation to crystalline phases might be of a great biological relevance. Namely, the initiating role ACPs play in matrix vesicle biomineralization raises the importance of this phase from a mere laboratory curiosity to that of a key intermediate in skeletal calcification. Furthermore, ACPs are very promising candidates to manufacture artificial bone grafts.