H2 has aroused significant attention as an unpolluted and renewable energy carrier. However, the efficient storage and controllable release of H2 are urgent to be addressed. Through the hydrogenation of CO2 (bicarbonate) to produce formic acid (formate) and reverse dehydrogenation reactions, a carbon-neutral formic acid-based hydrogen cycle system can be established. Given the excellent recyclability and facile separation of heterogeneous catalysis, the development of heterogeneous catalysts for these reversible interconversions is thoroughly summarized, with a special focus on the structure–activity relationship and the mechanistic insight. Finally, the challenges and opportunities surrounding the formic acid-based hydrogen cycle system are discussed. It is hoped that this review will provide guidance and an idea for the design and development of efficient heterogeneous catalysts for the carbon-neutral H2 storage and release system.