Natural carbohydrate polymers such as starch, cellulose, and chitin provide renewable alternatives to fossil fuels as a source for fuels and materials. As such, there is considerable interest in their conversion for industrial purposes, which is evidenced by the established and emerging markets for products derived from these natural polymers. In many cases, this is achieved via industrial processes that use enzymes to break down carbohydrates to monomer sugars. One of the major challenges facing large-scale industrial applications utilizing natural carbohydrate polymers is rooted in the fact that naturally occurring forms of starch, cellulose, and chitin can have tightly packed organizations of polymer chains with low hydration levels, giving rise to crystalline structures that are highly recalcitrant to enzymatic degradation. The topic of this review is oxidative cleavage of carbohydrate polymers by lytic polysaccharide mono-oxygenases (LPMOs). LPMOs are copper-dependent enzymes (EC 1.14.99.53-56) that, with glycoside hydrolases, participate in the degradation of recalcitrant carbohydrate polymers. Their activity and structural underpinnings provide insights into biological mechanisms of polysaccharide degradation.