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Hybrid organic–inorganic perovskites (HOIPs) can have a diverse range of compositions including halides, azides, formates, dicyanamides, cyanides and dicyanometallates. These materials have several common features, including their classical ABX 3 perovskite architecture and the presence of organic amine cations that occupy the A-sites. Current research in HOIPs tends to focus on metal halide HOIPs, which show promise for use in solar cells and optoelectronic devices; however, the other subclasses also exhibit a diverse range of physical properties. In this Review, we summarize the chemical variability and structural diversity of all known HOIP subclasses. We also present a comprehensive account of their intriguing physical properties, including photovoltaic and optoelectronic properties, dielectricity, magnetism, ferroelectricity, ferroelasticity and multiferroicity. Moreover, we discuss the current challenges …