We present here a route to produce microporous organic polymers based on the step growth polycondensation of dichloroxylene and other bischloromethyl monomers. We show that materials with very high surface areas (∼1900 m2/g BET; ∼3000 m2/g Langmuir) can be obtained by varying the structure of the monomer. The resulting materials can physisorb up to around 3.7 wt. % H2 at 77 K and 15 bar - the highest value yet reported for an organic polymer. We have used a combination of solid-state NMR, gas sorption measurements, and atomistic simulations in order to rationalize the surface area, pore size, and H2 sorption properties of these polymers. We believe that this flexible methodology represents an important advance for the future design of purely organic sorbents with enhanced gas storage capacities.