Amorphous calcium phosphates (ACPs) represent a unique class of biomedically relevant calcium orthophosphate salts, having variable chemical but essentially identical glass-like physical properties, in which there is neither translational nor orientational long-range ordering of the atomic positions. Normally, ACPs are the first solid phases, precipitated after a rapid mixing of aqueous solutions containing ions of Ca(2+) and PO₄³⁻; however, other production techniques are known. Interestingly, ACPs prepared by wet-chemical techniques were found to have a relatively constant chemical composition over a relatively wide range of preparation conditions, which suggests the presence of a well-defined local structural unit, presumably with the structure of Ca₉(PO₄)₆ - so-called Posner cluster. However, the presence of similar clusters in ACPs produced by other techniques remains uncertain. All ACPs are thermodynamically unstable compounds and, unless stored in dry conditions or doped by stabilizers, spontaneously tend to transform to crystalline calcium orthophosphates, mainly to calcium apatites. This solution instability of ACPs and their easy transformation to crystalline phases are of a great biological relevance. Specifically, the initiating role ACPs play in matrix vesicle biomineralization raises the importance of ACPs from a mere laboratory curiosity to that of a key intermediate in skeletal calcification. In addition, due to significant chemical and structural similarities with calcified mammalian tissues, as well as excellent biocompatibility and bioresorbability, all types of ACPs are very promising candidates for the manufacture of artificial bone grafts. This review summarizes the current knowledge on the occurrence, preparation, composition, structure, major properties and biomedical applications of ACPs. To assist readers in looking for the specific details on ACPs, a great number of references have been collected and systematized.