The selective hydrogenation of unsaturated aldehydes (UAL) to saturated aldehydes (SAL) and unsaturated alcohols (UOL) is an important industrial process for producing fine chemicals. More efforts were made on the selective hydrogenation of CO to UOL, because CC hydrogenation is thermodynamically favored over CO hydrogenation. A crucial step toward high selectivity is the rational design of heterogeneous catalysts. In this Review, the catalyst design for the hydrogenation of UAL to UOL are catalogued into three major strategies, namely, modifying electronic properties, forming electrophilic sites, and involving confinement/steric effect. Research works accomplished in the past decade on the catalyst design for UAL hydrogenation are systematically reviewed using the above strategies. The focus is on the selectivity-enhancing mechanism, methods to perform the chosen strategy, and the factors that influence the mechanism. Density functional theory calculations and catalyst stability are discussed to appreciate the challenges in designing catalysts. In addition, recent advances in the selective hydrogenation of CC of cinnamaldehyde to hydrocinnamaldehyde are briefly reviewed.