The bulk terrestrial biomass resource in a future bio-economy will be lignocellulosic biomass, which is recalcitrant and challenging to process. Enzymatic conversion of polysaccharides in the lignocellulosic biomass will be a key technology in future biorefineries and this technology is currently the subject of intensive research. We describe recent developments in enzyme technology for conversion of cellulose, the most abundant, homogeneous and recalcitrant polysaccharide in lignocellulosic biomass. In particular, we focus on a recently discovered new type of enzymes currently classified as CBM33 and GH61 that catalyze oxidative cleavage of polysaccharides. These enzymes promote the efficiency of classical hydrolytic enzymes (cellulases) by acting on the surfaces of the insoluble substrate, where they introduce chain breaks in the polysaccharide chains, without the need of first "extracting" these chains from their crystalline matrix.