Selective hydrogenation of unsaturated aldehydes/ketones (UAL) to unsaturated alcohols (UOL) is a crucial reaction process in the fine chemical industry. Numerous efforts have been made to hydrogenate the target C--O group to UOL due to the C--C bond being more sensitive to reduction from both kinetics and thermodynamics. The key issue to designing catalysts with high performance is investigating and determining the structureperformance relationship in the selective hydrogenation of UAL. In this Review, the adsorption and activation mechanism of the reactants, and the influences of catalysts structures (electronic effects, synergistic effects, interfacial effects, and geometric effects) are comprehensively discussed. Additionally, the single-atom site catalysts and related catalysts including single-atom-site catalysts, dual-atom-site catalysts, nano-single-atom-site catalysts, and single-atom alloys, that applicated in UAL selective hydrogenation are systematically reviewed with a focus on the selective-enhancing mechanism. Finally, a brief perspective is provided to demonstrate the challenges as well as opportunities for rational designing advanced catalysts toward selective hydrogenation of UAL to UOL.