Lytic polysaccharide monooxygenases (LPMOs) are copper enzymes discovered within the last 10 years. By degrading recalcitrant substrates oxidatively, these enzymes are major contributors to the recycling of carbon in nature and are being used in the biorefinery industry. Recently, two new families of LPMOs have been defined and structurally characterized, AA14 and AA15, sharing many of previously found structural features. However, unlike most LPMOs to date, AA14 degrades xylan in the context of complex substrates, while AA15 is particularly interesting because they expand the presence of LPMOs from the predominantly microbial to the animal kingdom. The first two neutron crystallography structures have been determined, which, together with high-resolution room temperature X-ray structures, have putatively identified oxygen species at or near the active site of LPMOs. Many recent computational and experimental studies have also investigated the mechanism of action and substrate-binding mode of LPMOs. Perhaps, the most significant recent advance is the increasing structural and biochemical evidence, suggesting that LPMOs follow different mechanistic pathways with different substrates, co-substrates and reductants, by behaving as monooxygenases or peroxygenases with molecular oxygen or hydrogen peroxide as a co-substrate, respectively.