Biomass is viewed as an important renewable carbon source, in which 5‐hydroxymethylfurfural (HMF) plays an important role as platform compound. 2, 5‐dihydroxymethylfuran (DHMF) and 2, 5‐dimethylfuran (DMF) could be obtained by the hydrogenation of HMF under certain conditions. The DHMF and DMF are chemicals of high added value with wide application.The catalysts played a key role in the conversion of HMF to DHMF and DMF. This review paid attentions on the hydrogenation of HMF to DHMF and the hydrogenolysis of HMF to DMF via kinds of catalytic systems. The recent progress were summarized according to catalytic system, including noble metal catalysts and non‐noble metal catalysts and a perspective on the transformation was given based on the recent progress.