Organic open frameworks with well-defined micropore (pore dimensions below 2 nm) structure are attractive next-generation materials for gas sorption, storage, catalysis and molecular level separations. Polymers of intrinsic microporosity (PIMs) represent a paradigm shift in conceptualizing molecular sieves from conventional ordered frameworks to disordered frameworks with heterogeneous distributions of microporosity. PIMs contain interconnected regions of micropores with high gas permeability but with a level of heterogeneity that compromises their molecular selectivity. Here we report controllable thermal oxidative crosslinking of PIMs by heat treatment in the presence of trace amounts of oxygen. The resulting covalently crosslinked networks are thermally and chemically stable, mechanically flexible and have remarkable selectivity at permeability that is three orders of magnitude higher than commercial polymeric membranes. This study demonstrates that controlled thermochemical reactions can delicately tune the topological structure of channels and pores within microporous polymers and their molecular sieving properties.