With the price-competitiveness of solar and wind power, hydrogen technologies may be game changers for a cleaner, defossilized, and sustainable energy future. H2 can indeed be produced in electrolyzers from water, stored for long periods, and converted back into power, on demand, in fuel cells. The feasibility of the latter process critically depends on the discovery of cheap and efficient catalysts able to replace platinum group metals at the anode and cathode of fuel cells. Bioinspiration can be key for designing such alternative catalysts. Here we show that a novel class of iron-based catalysts inspired from the active site of [FeFe]-hydrogenase behave as unprecedented bidirectional electrocatalysts for interconverting H2 and protons efficiently under near-neutral aqueous conditions. Such bioinspired catalysts have been implemented at the anode of a functional membrane-less H2/O2 fuel cell device.