ReO 3-type structures can be described as ABX 3 perovskites in which the A-cation site is unoccupied. They therefore have the general composition BX 3 , where B is normally a cation and X is a bridging anion. The chemical diversity of such structures is very broad, ranging from simple oxides and fluorides, such as WO 3 and AlF 3 , to more complex systems in which the bridging anion is polyatomic, as in the Prussian blue-related cyanides such as Fe(CN) 3 and CoPt(CN) 6. The same topology is also found in metal-organic frameworks, for example In(Im) 3 (Im = imidazolate), and even the well-known MOF-5 structure, where the B-site cation is itself polyatomic. This remarkable chemical diversity gives rise to a wide range of interesting and often unusual properties, including negative thermal expansion (ScF 3), photocatalysis (CoSn(OH) 6), thermoelectricity (CoAs 3), and even a report of superconductivity in a phase that is controversially described as SH 3 with a doubly interpenetrating ReO 3 structure. We present a comprehensive account of this exciting family of materials and discuss current challenges and future opportunities in the area.