Membranes utilizing nanoporous one-dimensional (1D) and two-dimensional (2D) materials are emerging as attractive candidates for applications in molecular separations and related areas. Such nanotubular and nanolayered materials include carbon nanotubes, metal oxide nanotubes, layered zeolites, porous layered oxides, layered aluminophosphates, and porous graphenes. By virtue of their unique shape, size, and structure, they possess transport properties that are advantageous for membrane and thin film applications. These materials also have very different chemistry from more conventional porous 3D materials, due to the existence of a large, chemically active, external surface area. This feature also necessitates the development of innovative strategies to process these materials into membranes and thin films with high performance. This work provides the first comprehensive review of this emerging area. We first discuss approaches for the synthesis and structural characterization of nanoporous 1D and 2D materials. Thereafter, we elucidate different approaches for fabrication of membranes and thin films from these materials, either as multiphase (composite/hybrid) or single-phase membranes. The influence of surface chemistry and processing techniques on the membrane morphology is highlighted. We then discuss the applications of such membranes in areas relating to molecular transport and separation, e.g. gas and liquid-phase separations, water purification, and ion-conducting membranes. The review concludes with a discussion of the present outlook and some of the key scientific challenges to be addressed on the path to industrially applicable membranes containing nanoporous 1D and 2D materials. © 2013 Elsevier Ltd.