Glucose oxidase enzymes are provided, including novel variants of galactose oxidase enzymes. The polynucleotides that encode these novel variants can be expressed in recombinant host cell expression systems. The novel variant oxidase enzymes are capable of oxidizing compounds towards which wild-type galactose oxidase (e.g. D-galactose: oxygen 6-oxidoreductase, GAO; EC 1.1.3.9) has little or no activity. Preferred galactose oxidase variants are those which that have improved capability to oxidize secondary alcohols and/or D-glucose relative to the wild-type enzyme.