Graphene and related materials (GRMs) are promising candidates for the fabrication of resistive random access memories (RRAM). Here, we analyze, classify and evaluate this emerging field, and summarize the performance of the RRAM prototypes using GRMs. Graphene oxide, amorphous carbon films, transition metal dichalcogenides, hexagonal boron nitride and black phosphorous can be used as resistive switching media, in which the switching can be governed either by the migration of intrinsic species or penetration of metallic ions from adjacent layers. Graphene can be used as electrode to provide flexibility and transparency, as well as an interface layer between the electrode and dielectric to block atomic diffusion, reduce power consumption, suppress surface effects, limit the number of conductive filaments in the dielectric, and improve device integration. GRMs-based RRAMs fit some non-volatile memory technological requirements like low operating voltages <1V and switching times <10 ns but others, like retention >10 years, endurance >109 cycles and power consumption ~10 pJ/transition still remain a challenge. More technology-oriented studies including reliability and variability analyses may lead to the development of GRMs-based RRAMs with realistic possibilities of commercialization.