5-Hydroxymethylfurfural (5-HMF) as a triply catalytic product is a value-added refining chemical in industry production. 5-HMF as biomass feedstock enables to be transformed into other high-value industrial compounds, such as 2,5-furandicarboxylic acid (FDCA), 5-hydroxymethyl-2-furancarboxylic acid (HMFCA), 5-formyl-2-furancarboxylic acid (FFCA), 2,5-diformylfuran (DFF), 2,5-bis(aminomethyl)furan (BAMF), and 2,5-dimethylfuran (DMF). Hence, catalytic conversion of biomass into 5-HMF has been given much more attention by chemists. In this review, some latest studies about the conversion of cellulose to 5-HMF have been introduced systematically. Solid acids such as heterogeneous catalysts have been widely applied in the conversion of cellulose into 5-HMF. Therefore, some novel solid acids with Brønsted and/or Lewis acidic sites, such as sulfonated solid acids, carbon-based acids, and zeolite particles employed for biomass conversions are listed.