Nonvolatile memory devices based on hybrid inorganic/organic nanocomposites have emerged as excellent candidates for promising applications in next-generation electronic and optoelectronic devices. Among the various types of nonvolatile memory devices, organic bistable devices fabricated utilizing hybrid organic/inorganic nanocomposites have currently been receiving broad attention because of their excellent performance with high-mechanical flexibility, simple fabrication and low cost. The prospect of potential applications of nonvolatile memory devices fabricated utilizing hybrid nanocomposites has led to substantial research and development efforts to form various kinds of nanocomposites by using various methods. Generally, hybrid inorganic/organic nanocomposites are composed of organic layers containing metal nanoparticles, semiconductor quantum dots (QDs), core-shell semiconductor QDs, fullerenes, carbon nanotubes, graphene molecules or graphene oxides (GOs). This review article describes investigations of and developments in nonvolatile memory devices based on hybrid inorganic/organic nanocomposites over the past 5 years. The device structure, fabrication and electrical characteristics of nonvolatile memory devices are discussed, and the switching and carrier transport mechanisms in the hybrid nonvolatile memory devices are reviewed. Furthermore, various flexible memory devices fabricated utilizing hybrid nanocomposites are described and their future prospects are discussed.