N-Methylation of lysine and arginine residues has emerged as a major mechanism of transcriptional regulation in eukaryotes. In humans, N-epsilon-methyllysine residue demethylation is catalysed by two distinct subfamilies of demethylases (KDMs), the flavin-dependent KDM1 subfamily and the 2-oxoglutarate- (2OG) dependent JmjC subfamily, which both employ oxidative mechanisms. Modulation of histone methylation status is proposed to be important in epigenetic regulation and has substantial medicinal potential for the treatment of diseases including cancer and genetic disorders. This article provides an introduction to the enzymology of the KDMs and the therapeutic possibilities and challenges associated with targeting them, followed by a review of reported KDM inhibitors and their mechanisms of action from kinetic and structural perspectives. This article is part of a Special Issue entitled: Methylation: A Multifaceted Modification looking at transcription and beyond. (C) 2014 Elsevier B.V. All rights reserved.