Abstract Pervaporation (PV), a membrane process in which the feed is a liquid mixture and the permeate is removed as a vapour, offers an energy-efficient alternative to conventional separation processes such as distillation, and can be applied to mixtures that are difficult to separate, such as azeotropes. Here the principles of pervaporation and its industrial applications are outlined. Two classes of material that show promise for use in PV membranes are described: Polymers of intrinsic microporosity (PIMs) and 2D materials such as graphene. The literature regarding PV utilizing the prototypical PIM (PIM-1) and it hydrophilic hydrolysed form (cPIM-1) is reviewed. Self-standing PIM-1 membranes give competitive results compared to other membranes reported in the literature for the separation of alcohols and other volatile organic compounds from aqueous solution, and for organic/organic separations such as methanol/ethylene glycol and dimethyl carbonate/methanol mixtures. Blends of cPIM-1 with conventional polymers improve the flux for dehydration of alcohols. The incorporation of fillers, such as functionalised graphene-like fillers, into PIM-1 to form mixed matrix membranes can enhance the separation performance. Thin film composite (TFC) membranes enable very high fluxes to be achieved when a suitable support with high surface porosity is utilised. When functionalised graphene-like fillers are introduced into the selective layer of a TFC membrane, the lateral size of the flakes needs to be carefully controlled. There is a wide range of PIMs and 2D materials yet to be explored for PV applications, which offer potential to create bespoke membranes for a wide variety of organic/aqueous and organic/organic separations.