This invention relates generally to membranes comprising an array of single-wall carbon nanotubes (SWNT) wherein the membrane is nanoporous. In one embodiment, the membrane comprises a substantially two-dimensional array of a homogeneous population of single-walled nanotubes aggregated in substantially parallel orientation to form a monolayer extending in directions substantially perpendicular to the orientation of the individual nanotubes. Using single-wall carbon nanotubes of the same type and structure provides a homogeneous array. By using different single-wall carbon nanotubes, either a random or ordered heterogeneous structure can be produced by employing successive reactions after removal of previously masked areas of a substrate. Other embodiments of the invention include batteries comprising a membrane comprising an array of single-wall carbon nanotubes or carbon fibers that are aggregates of single-wall carbon nanotubes, and wherein the plurality of single-wall carbon nanotubes are in a generally parallel orientation.