Today, chemistry and nanotechnology cover molecular separations in liquid and gas states by aiding in the design of new nano-sized materials. In this regard, the synthesis and application of two-dimensional (2D) nanomaterials are current fields of research in which structurally defined 2D materials are being used in membrane separation either in self-standing membranes or composites with polymer phases. For instance, pervaporation (PV), as a highly selective technology for liquid separation, benefits from using 2D materials to selectively transport water or other solvent molecules. Therefore, this review paper offers an interesting update in revising the ongoing progress of PV membranes using 2D materials in several applications, including solvent purification (the removal of water from organic systems), organics removal (the removal of organic molecules diluted in water systems), and desalination (selective water transport from seawater). In general, recent reports from the past 3 years have been discussed and analyzed. Attention has been devoted to the proposed strategies and fabrication of membranes for the inclusion of 2D materials into polymer phases. Finally, the future trends and current research gaps are declared for the scientists in the field.