Hydrogen gas is a storable form of chemical energy that could complement intermittent renewable energy conversion. One of the main disadvantages of hydrogen gas arises from its low density, and therefore, efficient handling and storage methods are key factors that need to be addressed to realize a hydrogen-based economy. Storage systems based on liquids, in particular, formic acid and alcohols, are highly attractive hydrogen carriers as they can be made from CO2 or other renewable materials, they can be used in stationary power storage units such as hydrogen filling stations, and they can be used directly as transportation fuels. However, to bring about a paradigm change in our energy infrastructure, efficient catalytic processes that release the hydrogen from these molecules, as well as catalysts that regenerate these molecules from CO2 and hydrogen, are required. In this review, we describe the considerable progress that has been made in homogeneous catalysis for these critical reactions, namely, the hydrogenation of CO2 to formic acid and methanol and the reverse dehydrogenation reactions. The dehydrogenation of higher alcohols available from renewable feedstocks is also described. Key structural features of the catalysts are analyzed, as is the role of additives, which are required in many systems. Particular attention is paid to advances in sustainable catalytic processes, especially to additive-free processes and catalysts based on Earth-abundant metal ions. Mechanistic information is also presented, and it is hoped that this review not only provides an account of the state of the art in the field but also offers insights into how superior catalytic systems can be obtained in the future.