Organic solvents are widely used in a variety of industrial sectors. Reclaiming and reusing the solvents may be the most economically and environmentally beneficial option for managing spent solvents. Purifying the solvents to meet reuse specifications can be challenging. For hydrophilic solvents, water must be removed prior to reuse, yet many hydrophilic solvents form hard‐to‐separate azeotropic mixtures with water. Such mixtures make separation processes energy‐intensive and cause economic challenges. The membrane processes pervaporation (PV) and vapor permeation (VP) can be less energy‐intensive than distillation‐based processes and have proven to be very effective in removing water from azeotropic mixtures. In PV/VP, separation is based on the solution–diffusion interaction between the dense permselective layer of the membrane and the solvent/water mixture. This review provides a state‐of‐the‐science analysis of materials used as the selective layer(s) of PV/VP membranes in removing water from organic solvents. A variety of membrane materials, such as polymeric, inorganic, mixed matrix, and hybrid, have been reported in the literature. A small subset of these is commercially available and highlighted here: poly (vinyl alcohol), polyimides, amorphous perfluoro polymers, NaA zeolites, chabazite zeolites, T‐type zeolites, and hybrid silicas. The typical performance characteristics and operating limits of these membranes are discussed. Solvents targeted by the United States Environmental Protection Agency for reclamation are emphasized and ten common solvents are chosen for analysis: acetonitrile, 1‐butanol, N,N‐dimethyl formamide, ethanol, methanol, methyl isobutyl ketone, methyl tert‐butyl ether, tetrahydrofuran, acetone, and 2‐propanol. Published 2018. This article is a U.S. Government work and is in the public domain in the USA.