The preparation of membranes with high selectivity based on specific chemical properties such as size and charge would impact the efficiency of the world's energy supply, the production of clean water, and many other separation technologies. We report a flexible synthetic protocol for preparing highly ordered two-dimensional nanoporous polymeric materials (termed covalent organic frameworks or COFs) that allow for placing virtually any function group within the nanopores. We demonstrate that membranes, fabricated with this new family of materials with carboxylated pore walls, are very water permeable, as well as highly charged and size selective.