Efficient CO₂ scrubbing without a significant energy penalty remains an outstanding challenge for the fossil fuel-burning industry where aqueous amine solutions are still widely used. Porous materials have long been evaluated for next generation CO₂ adsorbents. Porous polymers, robust and inexpensive, show promise as feasible materials for the capture of CO₂ from warm exhaust fumes. We report the syntheses of porous covalent organic polymers (COPs) with CO₂ adsorption capacities of up to 5616 mg g⁻¹ (measured at high pressures, i.e. 200 bar) and industrially relevant temperatures (as warm as 65 °C). COPs are stable in boiling water for at least one week and near infinite CO₂/H₂ selectivity is observed.