Owing to the increasing need to mitigate excessive organic solvent waste, the efficient separation and recovery of organic solvents have received major research attention in recent years. The membrane-based organic solvent nanofiltration (OSN) process has demonstrated its feasibility in addressing this problem with low energy costs, compared to conventional separation techniques, such as adsorption, liquid-liquid extraction, and solvent evaporation. Recently, membranes made of 2D graphene-based materials have shown great promise because they attain high solvent flux and solute rejection using easy processing methods. Thus, this paper focuses on state-of-the-art studies of graphene-based membranes used in OSN processes, which include syntheses, characterizations, performance evaluations, membrane fouling, and simulation studies, in combination with the development of the "upper-bound" line to indicate the performance of graphene-based membranes. In this paper, critical challenges involved in the development of graphene-based membranes are also focused on and discussed to map out the future directions of these membranes in industrial OSN processes. In addition to OSN, this paper pertains to a broader audience in other separation processes, particularly in the fields of gas separation and water treatment.