Increasing water consumption and diminishing fresh water resources have created the need for new water treatment technologies to supply safe water for domestic and industrial needs. The development of polymeric nanofiltration (NF) membrane technology led to water treatment at lower operating pressures than that of reverse osmosis. NF membranes reject particles and multivalent ions, however, monovalent ions pass through them along with water molecules. Factors such as selectivity and permeability, and fouling also limit their application. Incorporating suitable nanomaterials with polymer membranes has solved major problems, such as biofouling, scaling, low flux rate, selectivity, and degradation. Recent studies reveal that nanoporous single layer graphene and stacked graphene oxide (GO) membranes with desired spacing between layers are capable of rejecting monovalent ions, and are promising materials for future nanofiltration-based desalination. GO has antifouling properties that are highly advantageous for improving membrane properties. The basic understanding of the mechanism of graphene-based nanofiltration have been reported mainly based on computational studies. Hence, a great deal of experimental research is essential to develop efficient graphene membrane-based desalination methods for practical use. In this review, we highlight various properties of graphene and its derivatives that are essential for improving salt rejection, flux, and antifouling.