The derivation of second-generation biofuels from non-edible biomass is viewed as crucial for establishing a sustainable bio-based economy for the future. The inertness of lignocellulosic biomass makes its breakdown for conversion into fuels and other compounds a challenge. Enzyme cocktails can be utilized in the bio-refinery for lignocellulose deconstruction but until recently their costs were regarded as high. Lytic polysaccharide monooxygenases (LPMOs) offer tremendous promise for further process improvements owing to their ability to boost the activity of biomass-degrading enzyme consortia. Combining data from multiple disciplines, progress has been made in understanding the biochemistry of LPMOs. We review the academic literature in this area and highlight some of the key questions that remain.