Lignocellulose constitutes a major component of discarded wastes from various industries viz. agriculture, forestry and municipal waste treatment. The potential use of lignocellulose from such types of biomass can be maximized by enzymatic degradation using glycoside hydrolases (GHs) and oxidative enzymes to produce renewable fuels. Nonetheless, besides the slow rate of degradation and low yields, lignocellulose is also physicochemically recalcitrant and costly to process, further limiting its mass utilization. Therefore, bioprospecting for microorganisms producing efficient lytic polysaccharide monooxygenases (LPMOs) to overcome these drawbacks may prove beneficial. The use of GHs and LPMOs can potentially help to circumvent some limitations in the conversion of lignocellulosic biomass into fermentable sugars. LPMOs are classified as family GH61 or family 33 carbohydrate-binding module (CBM33), whose unusual surface-exposed active site is bound to a copper (II) ion. To date, there are more than 20 known genes encoding cellulose-active LPMOs in bacteria and fungi, with diverse biological activities. Only by thorough comprehension of the diversity, enzymology and role of primary GHs, i.e. celullases and their oxidative machinery can the degradation of lignocellulosic biomass be improved. This review provides insight into the diversity, structure and mechanisms, structural and functional aspects of the oxidative breakdown of cellulose by LPMOs of the cellulose-active GH family.