The present invention is for high performance UV-cross-linked membranes from polymers of intrinsic microporosity (PIMs) and the use of such membranes for separations. More specifically, the invention involves the methods of making UV-cross-linked membranes from PIMs. These membranes were prepared by cross-linking the UV-cross-linkable membranes from PIMs by exposure to UV-radiation. Pure gas permeation test results demonstrate that the UV-cross-linked membranes from PIMs exhibit CO2/CH4 performance well above the Robeson's polymer upper bound trade-off curve for CO2/CH4 separation. They have more than doubled selectivity for CO2/CH4 and extremely high permeability of CO2 compared to the original UV-cross-linkable membranes from PIMs. These membranes also show excellent separation performance for CO2/N2, H2/CH4, O2/N2, and propylene/propane separations. These high performance UV-cross-linked membranes are very useful for gas and liquid separations such as CO2/CH4, CO2/N2, H2/CH4, O2/N2, olefin/paraffin, deep desulfurization of gasoline and diesel fuels, and ethanol/water separations.