We review recent progress in the computational study of graphene as an RO membrane.• We introduce graphene and current knowledge about its mass transport properties. • We examine six key mechanisms that govern salt rejection in graphene. • Molecular dynamics have played a dominant role in the study of graphene membranes. • We suggest a greater role for quantumlevel simulations and macroscale computation.In this review, we examine the potential and the challenges of designing an ultrathin reverse osmosis (RO) membrane from graphene, focusing on the role of computational methods in designing, understanding, and optimizing the relationship between atomic structure and RO performance. In recent years, graphene has emerged as a promising material for improving the performance of RO. Beginning at the atomic scale and extending to the RO plant scale, we review applications of computational research that have explored the structure, properties and potential performance of nanoporous graphene in the context of RO desalination.