Traditional chemotherapy against cancer is often severely hampered by acquired resistance to the drug. Epigenetic alterations and other mechanisms like drug efflux, drug metabolism, and engagement of survival pathways are crucial in evading drug pressure. Herein, growing evidence suggests that a subpopulation of tumor cells can often tolerate drug onslaught by entering a "persister" state with minimal proliferation. The molecular features of these persister cells are gradually unraveling. Notably, the "persisters" act as a cache of cells that can eventually re-populate the tumor post-withdrawal drug pressure and contribute to acquiring stable drug-resistant features. This underlines the clinical significance of the tolerant cells. Accumulating evidence highlights the importance of modulation of the epigenome as a critical adaptive strategy for evading drug pressure. Chromatin remodeling, altered DNA methylation, and de-regulation of non-coding RNA expression and function contribute significantly to this persister state. No wonder targeting adaptive epigenetic modifications is increasingly recognized as an appropriate therapeutic strategy to sensitize them and restore drug sensitivity. Furthermore, manipulating the tumor microenvironment and "drug holiday" is also explored to maneuver the epigenome. However, heterogeneity in adaptive strategies and lack of targeted therapies have significantly hindered the translation of epigenetic therapy to the clinics. In this review, we comprehensively analyze the epigenetic alterations adapted by the drug-tolerant cells, the therapeutic strategies employed to date, and their limitations and future prospects.