Metal-organic frameworks (MOFs) are crystalline nanoporous materials with a variety of potential applications in gas separations and storage. We have developed a hierarchical modeling approach to screen MOFs for membrane-based gas separations, an application that is challenging because it requires information on both adsorption affinity and molecular diffusivities. Our approach uses geometric characterization to screen hundreds of materials, then molecular modeling and quantum chemistry calculations to make detailed predictions about strong candidate materials. We will show examples of using this approach to develop materials for efficient separation of methane and carbon dioxide. We will also discuss selection and testing of MOFs for efficient separations of noble gases, an application that defines an ideal testbed for current computational and synthetic approaches to materials design with these materials.