Selective hydrogenation of α,β-unsaturated aldehydes to unsaturated alcohols is a challenging class of reactions, yielding valuable intermediates for the production of pharmaceuticals, perfumes, and flavorings. On monometallic heterogeneous catalysts, the formation of the unsaturated alcohols is thermodynamically disfavored over the saturated aldehydes. Hence, new catalysts are required to achieve the desired selectivity. Herein, the literature of three major research areas in catalysis is integrated as a step toward establishing the guidelines for enhancing the selectivity: reactor studies of complex catalyst materials at operating temperature and pressure, surface science studies of crystalline surfaces in ultrahigh vacuum, and first-principles modeling using density functional theory calculations. Aggregate analysis shows that bimetallic and dilute alloy catalysts significantly enhance the selectivity to the unsaturated alcohols compared to monometallic catalysts. This comprehensive review focuses primarily on the role of different metal surfaces as well as the factors that promote the adsorption of the unsaturated aldehyde via its C═O bond, most notably by electronic modification of the surface and formation of the electrophilic sites. Furthermore, challenges, gaps, and opportunities are identified to advance the rational design of efficient catalysts for this class of reactions, including the need for systematic studies of catalytic processes, theoretical modeling of complex materials, and model studies under ambient pressure and temperature.