Crystalline materials have governed the development of hybrid organic-inorganic perovskites (HOIPs), giving rise to a variety of fascinating applications such as solar cells and optoelectronic devices. With increasing interest in non-crystalline systems, the glassy state of HOIPs has recently been identified. Here, the basic building blocks of crystalline HOIPs appear to be retained, though their glasses lack long-range periodic order. The emerging family of glasses formed from HOIPs exhibits diverse properties, complementary to their crystalline state. This mini review describes the chemical diversity of both three-dimensional and two-dimensional crystalline HOIPs and demonstrates how glasses are produced from these materials. Specifically, current achievements in melt-quenched glasses formed from HOIPs are highlighted. We conclude with our perspective on the future of this new family of materials.