Multiple myeloma (MM) is a clonal plasma cell malignancy that develops primarily in the bone marrow (BM), where reciprocal interactions with the BM niche foster MM cell survival, growth, and drug resistance. MM cells furthermore reshape the BM to their own needs by affecting the different BM stromal cell types resulting in angiogenesis, bone destruction, and immune suppression. Despite recent advances in treatment modalities, MM remains most often incurable due to the development of drug resistance to all standard of care agents. This underscores the unmet need for these heavily treated relapsed/refractory patients. Disruptions in epigenetic regulation are a well-known hallmark of cancer cells, contributing to both cancer onset and progression. In MM, sequencing and gene expression profiling studies have also identified numerous epigenetic defects, including locus-specific DNA hypermethylation of cancer-related and B cell specific genes, genome-wide DNA hypomethylation and genetic defects, copy number variations and/or abnormal expression patterns of various chromatin modifying enzymes. Importantly, these so-called epimutations contribute to genomic instability, disease progression, and a worse outcome. Moreover, the frequency of mutations observed in genes encoding for histone methyltransferases and DNA methylation modifiers increases following treatment, indicating a role in the emergence of drug resistance. In support of this, accumulating evidence also suggest a role for the epigenetic machinery in MM cell plasticity, driving the differentiation of the malignant cells to a less mature and drug resistant state. This review discusses the current state of knowledge on the role of epigenetics in MM, with a focus on deregulated histone methylation modifiers and the impact on MM cell plasticity and drug resistance. We also provide insight into the potential of epigenetic modulating agents to enhance clinical drug responses and avoid disease relapse.