Photocatalytic hydrogen production from water offers an abundant, clean fuel source, but it is challenging to produce photocatalysts that use the solar spectrum effectively. Many hydrogen-evolving photocatalysts are active in the ultraviolet range, but ultraviolet light accounts for only 3% of the energy available in the solar spectrum at ground level. Solid-state crystalline photocatalysts have light absorption profiles that are a discrete function of their crystalline phase and that are not always tunable. Here, we prepare a series of amorphous, microporous organic polymers with exquisite synthetic control over the optical gap in the range 1.94-2.95 eV. Specific monomer compositions give polymers that are robust and effective photocatalysts for the evolution of hydrogen from water in the presence of a sacrificial electron donor, without the apparent need for an added metal cocatalyst. Remarkably, unlike other organic systems, the best performing polymer is only photoactive under visible rather than ultraviolet irradiation.