Histone lysine demethylases comprise an important family of epigenetic regulatory enzymes. They catalyse the demethylation of tri-, di- and monomethylated lysine residues on histone H3, thus contributing to either silencing or activation of chromatin. Their biological roles are widespread and have just begun to be elucidated. Among other functions, they contribute to establishment and maintenance of pluripotent states in embryonic stem cells, and also to cellular differentiation during development. Abnormal expression or mutation of some demethylases has been linked to diverse diseases, from prostate and oesophageal cancers to X-linked mental retardation. The development of small molecule inhibitors of histone demethylases is therefore of interest, both from the therapeutic perspective, and with the aim of developing chemical probes to understand the diverse functions of the demethylases in vivo. Most histone lysine demethylases belong to the 2-oxoglutarate and ferrous iron dependent dioxygenase superfamily. This family utilises molecular oxygen to catalyse hydroxylation of substrates, together with oxidation/decarboxylation of the 2-oxoglutarate cofactor. In the work outlined in this thesis, the JMJD2 family of histone demethylases was characterised biochemically, with attention given to mechanism, substrate selectivity and the role of eo factors. JMJD2E was identified herein as a novel histone demethylase in H. sapiens, and was shown to be selective for the demethylation of tri-, di- and monomethylated lysine 9 in histone H3. JMJD2E was also found to be particularly amenable to mechanistic and inhibition studies in vitro. A variety of mechanistic investigations established details of the catalytic cycle, its substrate selectivity and the role of iron and ascorbic acid as cofactors. Crystallographic analyses were also employed to compare its substrate selectivity to other JMJD2 family members. Assays suitable for the evaluation of inhibitors of the JMJD2 demethylases were then developed. These included a coupled enzyme assay suitable for kinetic measurements, and two mass spectrometric assays for observing inhibitor binding and catalytic activity. A critical review of the 20G oxygenase inhibitor literature carried out, and was then used as a basis for the identification of inhibitor scaffolds for the JMJD2 demethylases. These were characterised both in vitro (using kinetic assays, mass spectrometry and crystallography), and in cell culture. Some were further developed to achieve selective inhibition of the JMJD2 demethylases over the related prolyl hydroxylase PHD2; crystallography was again employed to understand the mode of inhibition of these potent inhibitors. The kinetic assays developed were optimised for use in a high-throughput screen, and a library of 240 000 compounds was screened against JMJD2E. This was the first instance of high-throughput screening against these promising therapeutic targets. Several hit compounds were identified and characterised further in vitro. Finally, alternative means of inhibiting the JMJD2 demethylases were investigated. Compounds were identified that inhibited JMJD2A by ejection of its unique structural zinc ion, thus demonstrating that selective inhibition of the JMJD2 demethylase family is possible. In summary, this work contains the first detailed investigation of a histone demethylase subfamily, and also the first steps towards identifying potent, selective inhibitors of these epigenetic regulatory enzymes.