The present invention discloses a new type of high performance polymer membranes prepared from aromatic polyimide membranes by thermal treating and crosslinking and methods for making and using these membranes. The polymer membranes were prepared from aromatic polyimide membranes by thermal treating under inert atmosphere followed by crosslinking preferably by using a UV radiation source. 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 membranes showed significantly improved selectivity and permeability for gas separations compared to the aromatic polyimide membranes without any treatment. The membranes can be fabricated into any convenient geometry and are not only suitable for a variety of liquid, gas, and vapor separations, but also can be used for other applications such as for catalysis and fuel cell applications.