Significant achievements have been made on the development of next-generation filtration and separation membranes using graphene materials, as graphene-based membranes can afford numerous novel mass-transport properties that are not possible in state-of-art commercial membranes, making them promising in areas such as membrane separation, water desalination, proton conductors, energy storage and conversion, etc. The latest developments on understanding mass transport through graphene-based membranes, including perfect graphene lattice, nanoporous graphene and graphene oxide membranes are reviewed here in relation to their potential applications. A summary and outlook is further provided on the opportunities and challenges in this arising field. The aspects discussed may enable researchers to better understand the mass-transport mechanism and to optimize the synthesis of graphene-based membranes toward large-scale production for a wide range of applications.