Safe and efficient hydrogen-carrying and -storing materials are in high demand for future hydrogen-based energy systems. Series of hydrogen carriers have been studied and examined, such as organic hydrides, metal hydrides and metal-organic frameworks; however, these carriers often suffer from safety issues and usually fix and store hydrogen at energy-consuming high pressures and/or temperatures. Here, we review organic polymers and their molecular design for hydrogen storage. Porous organic polymers, hypercrosslinked polymers and polymers with intrinsic microporosity reversibly stored and released hydrogen through hydrogen physisorption on their highly porous structures. Ketone and N-heterocycle polymers fixed and stored hydrogen at atmospheric pressure through the formation of chemical bonds to form the corresponding alcohol and hydrogenated N-heterocycle polymers, respectively. Electrochemical hydrogenation using water as a hydrogen source was also effective, in which the polymer worked as a scaffold for hydrogenation. The hydrogenated polymers released hydrogen in the presence of catalysts at mild conditions. The potential of using organic polymers in the quest for finding new types of hydrogen-carrying and -storing materials that are very safe and portable is suggested.