Heterogeneous catalytic conversion of lignocellulosic components into valuable chemicals and biofuels is one of the promising ways for biomass valorization, which well meets green chemistry metrics, and can alleviate environmental and economic issues caused by the rapid depletion of fossil fuels. Among the identified biomass derivatives, furfural (FF) and 5-hydroxymethylfurfural (HMF) stand out as rich building blocks and can be directly produced from pentose and hexose sugars, respectively. In the past decades, much attention has been attracted to the selective hydrogenation of FF and 5-hydroxymethylfurfural using various heterogeneous catalysts. This review evaluates the recent progress of developing different heterogeneous catalytic materials, such as noble/non-noble metal particles, solid acids/bases, and alkali metal salts, for the efficient reduction of bio-based furanic aldehydes to alcohols. Emphasis is laid on the insights and challenges encountered in those biomass transformation processes, along with the focus on the understanding of reaction mechanisms to clarify the catalytic role of specific active species. Brief outlook is also made for further optimization of the catalytic systems and processes for the upgrading of biofuranic compounds.