In comparison with traditional chemical separation processes, membrane separation is much simpler and more efficient. An ideal membrane for molecular separation should be as thin as possible to maximize its solvent flux, be mechanically robust to prevent it from fracture, and have well-defined pore sizes to guarantee its selectivity. Graphene is an excellent platform for developing size-selective membranes because of its atomic thickness, high mechanical strength, and chemical inertness. In this Perspective, we review the recent advancements on the fabrication of nanoporous graphene membranes and graphene oxide membranes (GOMs) for molecular separation. The methods of fabricating these membranes are summarized, and the mechanisms of molecular separation based on these two types of graphene membranes are compared. The challenges of synthesizing and transferring large-area nanoporous graphene membranes and engineering the performances of GOMs are discussed.