Membrane separation technologies have shown remarkable performance because of their higher selectivity and lower energy consumption as compared with conventional separation processes. However, the low chemical and thermal resistance of most polymeric membranes represent a serious drawback. Graphitic carbon materials have been widely used in the separation process, in response to their tunable physicochemical properties, high surface area, abundance, and low cost. In this dissertation, two-dimensional (2D) graphitic carbon materials such as graphene/graphene oxide (GO) were used in the membrane separation process. The engineering in the chemical structure, nanopore density, and morphology of 2D carbon-based materials allowed the modulation of the membrane's molecular sieving properties. Enhancing the performance and understanding of graphene-based membranes for solvent nanofiltration and water desalination.