Mounting evidence links genetic lesions with genome topology alterations and aberrant gene activation. However, the role of epigenetic plasticity remains elusive. Emerging studies implicate DNA methylation, transcriptional elongation, long noncoding RNAs (lncRNAs), and CCCTC-binding factor (CTCF)-RNA interactions, but systematic approaches are needed to fully decipher the role of epigenetic plasticity in genome integrity and function.