Amorphous calcium orthophosphates (ACPs) represent a unique class of biomedically relevant calcium or- thophosphate salts, having variable chemical but rather identical glass-like physical properties, in which there are neither translational nor orientational long-range orders of the atomic positions. Normally, ACPs are the first solid phases, precipi- tated after a rapid mixing of aqueous solutions containing ions of Ca 2+ and PO4 3- ; however, other production techniques are known. Interestingly, but ACPs prepared by wet-chemical techniques were found to possess a relative constancy in their chemical composition over a relatively wide range of preparation conditions, which suggested the presence of a well-defined local structural unit, presumably, with the structure of Ca9(PO4)6 - so-called a Posner's cluster. However, the presence of similar clusters in ACPs produced by other techniques remains uncertain. All ACPs are thermodynamically unstable com- pounds and, unless stored in dry conditions or doped by stabilizers, spontaneously they tend to transform to crystalline cal- cium orthophosphates, mainly to calcium apatites. This solution instability of ACPs and their easy transformation to crys- talline phases are of a great biological relevance. Namely, the initiating role ACPs play in matrix vesicle biomineralization raises the importance of ACPs from a mere laboratory curiosity to that of a reasonable key intermediate in skeletal calcifi- cation. In addition, due to great chemical and structural similarities to the calcified tissues of mammals, as well as excellent biocompatibility and bioresorbability, all types of ACPs are very promising candidates to manufacture artificial bone grafts. In this review, current knowledge on occurrence, preparation, composition, structure, major properties and biomedical ap- plications of ACPs have been summarized. To assist the readers in looking for the specific details on ACPs, a great number of references have been collected and systematized.