The pervasiveness of information technologies is generating an impressive amount of data, which need to be accessed very quickly. Nonvolatile memories (NVMs) are making inroads into high‐capacity storage to replace hard disk drives, fuelling the expansion of the global storage memory market. As silicon‐based flash memories are approaching their fundamental limit, vertical stacking of multiple memory cell layers, innovative device concepts, and novel materials are being investigated. In this context, emerging 2D materials, such as graphene, transition metal dichalcogenides, and black phosphorous, offer a host of physical and chemical properties, which could both improve existing memory technologies and enable the next generation of low‐cost, flexible, and wearable storage devices. Herein, an overview of graphene and related 2D materials (GRMs) in different types of NVM cells is provided, including resistive random‐access, flash, magnetic and phase‐change memories. The physical and chemical mechanisms underlying the switching of GRM‐based memory devices studied in the last decade are discussed. Although at this stage most of the proof‐of‐concept devices investigated do not compete with state‐of‐the‐art devices, a number of promising technological advancements have emerged. Here, the most relevant material properties and device structures are analyzed, emphasizing opportunities and challenges toward the realization of practical NVM devices.