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 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.We acknowledge support from the Young 1000 Global Talent Recruitment Program of the Ministry of Education of China, the National Natural Science Foundation of China (grants no. 61502326, 41550110223), the Jiangsu Government (grant no. BK20150343), the Ministry of Finance of China (grant no. SX21400213), the Young 973 National Program of the Chinese Ministry of Science and Technology (grant no. 2015CB932700), the Collaborative Innovation Center of Suzhou Nano Science & Technology, the Jiangsu Key Laboratory for Carbon-Based Functional Materials & Devices, the Priority Academic Program Development of Jiangsu Higher Education Institutions, the National Natural Science Foundation of China under Grant Nos. 61521064, 61322408, 61422407, the Beijing Training Project for the Leading Talents in S&T under Grant No. ljrc201508, the Opening Project of Key Laboratory of Microelectronic Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, the EU Graphene Flagship, FP7 Grant CARERAMM, ERC Grants Hetero2D and Highgraink, EPSRC Grants EP/K01711X/1, EP/K017144/1, EP/N010345/1, EP/M507799/1, EP/L016087/1, EP/M013243/1