Higher alcohol (HA) synthesis via the hydrogenation of CO₂ constitutes a relatively new and exciting field of research that has the potential to help towards the de-carbonization of the energy sector. The process poses formidable challenges, as it demands the formation of at least one C-C bond, when CO₂ is thermodynamically stable, fully oxidized and kinetically inert. This work provides a comprehensive and critical literature review of the catalytic formulations that have been employed, in both fixed-bed and batch reactors, which include noble metal catalysts, transition metal-based systems, post-transition metal catalysts, bimetallic, multimetallic/multifunctional catalysts, Metal Organic Frameworks (MOFs), perovskite-, and zeolite-based catalysts. The critical role of promoters and supports and the effect that the reaction conditions have on performance are also discussed. Emphasis has been given to single atom catalysts (SACs), as the high specific activity of these systems seems to hold great promise for the reaction at hand. Breakthroughs made by employing the concept of tandem catalysis are also critically analyzed. This review paper also discusses the thermodynamic aspects of the reaction and the insights that have been gained regarding the reaction mechanism. Finally, it provides an overview of the direction that research may move to into the future.