The catalytic hydrogenation of esters and carboxylic acids represents a fundamental and important class of organic transformations, which is widely applied in energy, environmental, agricultural, and pharmaceutical industries. Due to the low reactivity of the carbonyl group in carboxylic acids and esters, this type of reaction is, however, rather challenging. Hence, specifically active catalysts are required to achieve a satisfactory yield. Nevertheless, in recent years, remarkable progress has been made on the development of catalysts for this type of reaction, especially heterogeneous catalysts, which are generally dominating in industry. Here in this review, we discuss the recent breakthroughs as well as milestone achievements for the hydrogenation of industrially important carboxylic acids and esters utilizing heterogeneous catalysts. In addition, related catalytic hydrogenations that are considered of importance for the development of cleaner energy technologies and a circular chemical industry will be discussed in detail. Special attention is paid to the insights into the structure-activity relationship, which will help the readers to develop rational design strategies for the synthesis of more efficient heterogeneous catalysts.