In the energy transition context, there is growing interest in thermochemical catalytic processes for producing synthetic renewable hydrocarbons. These include biomass gasification followed by syngas conversion, or CO₂ capture from flue gases and subsequent hydrogenation—known as carbon capture and utilization (CCU). The latter uses excess renewable electricity to generate green hydrogen via water electrolysis, a concept called Power-to-Fuel. A recently proposed approach, sorption-enhanced hydrogenation, applies Le Chatelier’s principle to improve reaction efficiency by selectively removing steam with a suitable sorbent. By locally adsorbing water, the system shifts equilibrium toward desired products, enabling effective hydrogenation at relatively low pressures. The key challenge is developing materials that adsorb water under relevant operating conditions yet can be regenerated without degrading the catalyst or consuming excessive energy. Most research so far has focused on fixed-bed reactors, which are simple and compact but require intermittent operation for sorbent regeneration and face heat management challenges at larger scale. In contrast, chemical looping systems using coupled fluidized beds can offer continuous operation, easier heat control, and effective sorbent regeneration. This review summarizes both early and recent developments in sorption-enhanced catalytic hydrogenation of carbon oxides into products such as methane, methanol, dimethyl ether, and carbon monoxide (via the reverse water-gas shift reaction). It covers experimental and modeling studies, and highlights key challenges and research directions for scaling up this promising technology to commercial levels.