The catalytic conversion of biomass-derived 5-hydroxymethylfurfural (HMF) has been extensively studied due to its potential to produce a range of valuable chemicals and fuels through the selective hydrogenation/hydrodeoxynation of C=O, C=C or C–O bonds. The research has primarily focused on improving reaction rates and controlling product selectivity by designing highly efficient heterogeneous catalysts. It is well established that catalytic activity and selectivity are strongly depending on the electronic and geometric structures of the active species of metal supported catalysts. These structural features play a critical role in governing the adsorption and activation of reactant and H2 molecules during reactions. This paper provides a comprehensive review of recent advancements in HMF conversion over the past decades, with a particular emphasis on elucidating the catalytic mechanisms of bimetallic catalysts. The key factors, which influence the selective activation of C=O, C=C and C–O bonds, such as the electronic interactions of active metal species (including bimetallic alloys and intermetallic compounds), and the structural interactions of active species with support (encapsulation, metal-N(S) species and oxygen vacancies), surface acidity (originating from doped secondary metals or inherent acidity of the supports), will be systematically discussed and summarized.