Lytic polysaccharide monooxygenases (LPMOs) are mononuclear copper enzymes that catalyse the oxidative cleavage of glycosidic bonds. They are characterised by two histidine residues that coordinate copper in a configuration termed the Cu-histidine brace. Although first identified in bacteria and fungi, LPMOs have since been found in all biological kingdoms. LPMOs are now included in commercial enzyme cocktails used in industrial biorefineries. This has led to increased process yield due to the synergistic action of LPMOs with glycoside hydrolases. However, the introduction of LPMOs makes control of the enzymatic step in industrial stirred-tank reactors more challenging, and the operational stability of the enzymes is reduced. It is clear that much is still to be learned about the interaction between LPMOs and their complex natural and industrial environments, and fundamental scientific studies are required towards this end. Several atomic-resolution structures have been solved providing detailed information on the Cu-coordination sphere and the interaction with the polysaccharide substrate. However, the molecular mechanisms of LPMOs are still the subject of intense investigation; the key question being how the proteinaceous environment controls the copper cofactor towards the activation of the O-O bond in O₂ and cleavage of the glycosidic bonds in polysaccharides. The need for biochemical characterisation of each putative LPMO is discussed based on recent reports showing that not all proteins with a Cu-histidine brace are enzymes.