Intrinsically ultramicroporous (<7 Å) polymers represent a new paradigm in materials development for membrane-based gas separation. In particular, they demonstrate that uniting intrachain "rigidity", the traditional design metric of highly permeable polymers of intrinsic microporosity (PIMs), with gas-sieving ultramicroporosity yields high-performance gas separation membranes. Highly ultramicroporous PIMs have redefined the state-of-the-art in large-scale air (e.g., O2/N2) and hydrogen recovery (e.g., H2/N2, H2/CH4) applications with unprecedented molecular sieving gas transport properties. Accordingly, presented herein are new 2015 permeability/selectivity "upper bounds" for large-scale commercial membrane-based air and hydrogen applications that accommodate the substantial performance enhancements of recent PIMs over preceding polymers. A subtle balance between intrachain rigidity and interchain spacing has been achieved in the amorphous microstructures of PIMs, fine-tuned using unique bridged-bicyclic building blocks (i.e., triptycene, ethanoanthracene and Tröger's base) in both ladder and semiladder (e.g., polyimide) structures.