Hybrid organic-inorganic perovskites (HOIPs) can have a diverse range of compositions. These materials have several common features, including their classical ABX3 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. Moreover, we discuss the current challenges and future opportunities in this exciting field.