The stereochemistry of fluorides will be discussed in terms of dimensionality. This dimensionality, from 0D to 3D, is related to the connectivity of the building MX n m− units containing the metal M (M = aluminum, transition metal, or rare earth elements, X = F, O, N, S). These building units share eventually one, two, or three fluorine or oxygen atoms (corner, edge, or face of the MX n m− polyhedra) to form limited polyanions, infinite chains or layers, or a 3D network. Consequently, the structures will be presented according to their dimensionality, to their structural family, and to the nature of the building units. Imaginative associations of the building units will be eventually used to homogenize the structural descriptions. At the end of each section, some outstanding physical properties will be briefly presented and related to the structural data: ionic conductivity, superconductivity, ferroelasticity, and magnetism.The reader should be aware that the IUPAC nomenclature suggests "fluorido" instead of "fluoro" that is used all along this Review. All crystal structure projections were realized with Diamond software (Diamond -Crystal and Molecular Structure