Graphene family nanomaterials including single-layer graphene, multi-layer graphene, graphene quantum dots, graphene nanoplatelets, graphene oxide, and so forth demonstrate many excellent characteristics along with great thermal conductivity. Consequently, they are appropriate candidates for utilization in nanofluids and have recently received major attention in this area. Although many studies have been performed on graphene-based nanofluids, there is no thorough review article in which effective mechanisms on revealing enhancements and failures of graphene nanofluids are surveyed. Concerning various progress and problems existing in the field of graphene nanofluids, performing a complete review in this context is highly required, and there are still a lot of challenges that should be evaluated. In this review paper, the capabilities of graphene-based nanofluids are examined, and new developments on preparation techniques, stability improvement, and types of surfactants utilized are reviewed. Thermophysical properties, convective heat transfer, boiling, hydrodynamic attributes, and second law characteristics of graphene-family nanofluids are also investigated. Moreover, approaches such as molecular dynamics and artificial intelligence used in this field are reported and discussed. In addition, applications including use of graphene-based nanofluids in car radiators, heat exchangers, solar thermal, heat pipes, electronics cooling, and energy storage are presented. This in-depth review also identifies available challenges and recommends several directions for future research in this field. Finally, it is concluded that graphene family materials can improve the characteristics of base fluids considerably.