C4 and C5 diols and alcohols are important commodity chemicals mainly used as monomers in the production of polyesters, polyurethanes and polyethers. C4 and C5, on the other hand, can be used in the fuel industry for the preparation of additives to boost the gasoline octane number. The present critical review covers those reports describing the obtainment of these diols and alcohols from precursors derived from biomass. Emphasis is made on the description of the catalysts required for these transformations and on common traits referring to the bifunctionality combining hydrogenation activity and acidity and on the mechanistic proposals. The need for finding a suitable replacement for noble metals on the composition of these catalysts has been remarked throughout the review.