IDH1 and IDH2 mutations occur frequently in gliomas and acute myeloid leukemia, leading to simultaneous loss and gain of activities in the production of $\alpha$-ketoglutarate ($\alpha$-KG) and 2-hydroxyglutarate (2-HG), respectively. Here we demonstrate that 2-HG is a competitive inhibitor of multiple $\alpha$-KG-dependent dioxygenases, including histone demethylases and the TET family of 5-methlycytosine (5mC) hydroxylases. 2-HG occupies the same space as $\alpha$-KG does in the active site of histone demethylases. Ectopic expression of tumor-derived IDH1 and IDH2 mutants inhibits histone demethylation and 5mC hydroxylation. In glioma, IDH1 mutations are associated with increased histone methylation and decreased 5-hydroxylmethylcytosine (5hmC). Hence, tumor-derived IDH1 and IDH2 mutations reduce $\alpha$-KG and accumulate an $\alpha$-KG antagonist, 2-HG, leading to genome-wide histone and DNA methylation alterations.