Multiple myeloma (MM) is a hematological malignancy, which remains incurable because most patients eventually relapse or become refractory to current treatments. Due to heterogeneity within the cancer cell microenvironment, cancer cell populations employ a dynamic survival strategy to chemotherapeutic treatments, which frequently results in a rapid acquisition of therapy resistance. Besides resistance-conferring genetic alterations within a tumor cell population selected during drug treatment, recent findings also reveal non-mutational mechanisms of drug resistance, involving a small population of "cancer stem cells" (CSCs) which are intrinsically more refractory to the effects of a variety of anticancer drugs. Other studies have implicated epigenetic mechanisms in reversible drug tolerance to protect the population from eradication by potentially lethal exposures, suggesting that acquired drug resistance does not necessarily require a stable heritable genetic alteration. Clonal evolution of MM cells and the bone marrow microenvironment changes contribute to drug resistance. MM-CSCs may not be a static population and survive as phenotypically and functionally different cell types via the transition between stem-like and non-stem-like states in local microenvironments, as observed in other types of cancers. Targeting MM-CSCs is clinically relevant, and different approaches have been suggested to target molecular, metabolic and epigenetic signatures, and the self-renewal signaling characteristic of MM CSC-like cells. Here, we summarize epigenetic strategies to reverse drug resistance in heterogeneous multiple myeloma.