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. (C) 2015 Elsevier B.V. All rights reserved.