Alkanediols with five and six carbon atoms (1,2- & 1,5-pentanediols and 1,2- & 1,6-hexanediols, respectively) are an important class of industrial chemicals having wide application. Their production from lignocellulosic biomass-derived furfural and its derivatives using solid catalysts is a sustainable and attractive approach. Several bifunctional catalysts with metal (for hydrogenation/hydrogenolysis) and acid/base (for ring opening) functionalities have been reported. Effective and selective conversion of furfurals to a desired diol is still a challenge. This review discusses the recent advances in catalyst development for pentane- and hexanediols. The reaction pathways, active sites, and possible reaction mechanisms over the solid catalysts are discussed. A comparative catalytic activity data of the known catalysts are reported.