The present invention discloses a new type of high performance polymer membranes derived from aromatic polyimide membranes and methods for making and using these membranes. The polymer membranes described in the present invention were derived from aromatic polyimide membranes by crosslinking followed by thermal treating. The aromatic polyimide membranes were made from aromatic polyimide polymers comprising both pendent hydroxy functional groups ortho to the heterocyclic imide nitrogen and cross-linkable functional groups in the polymer backbone. The high performance polymer membranes showed significantly improved permeability for gas separations compared to the aromatic polyimide membranes without any treatment. The high performance polymer membranes also showed significantly improved selectivity for gas separations compared to the thermal-treated but non-UV-crosslinked aromatic polyimide membranes. The high performance polymer membranes of the present invention are suitable for liquid, gas, and vapor separations, as well as for catalysis and fuel cell applications.