Chromatin and associated epigenetic mechanisms stabilize gene expression and cellular states while also facilitating appropriate responses to developmental or environmental cues. Genetic, environmental, or metabolic insults can induce overly restrictive or overly permissive epigenetic landscapes that contribute to pathogenesis of cancer and other diseases. Restrictive chromatin states may prevent appropriate induction of tumor suppressor programs or block differentiation. By contrast, permissive or "plastic" states may allow stochastic oncogene activation or nonphysiologic cell fate transitions. Whereas many stochastic events will be inconsequential "passengers," some will confer a fitness advantage to a cell and be selected as "drivers." We review the broad roles played by epigenetic aberrations in tumor initiation and evolution and their potential to give rise to all classic hallmarks of cancer.