Multiple myeloma (MM) is still an incurable disease, despite considerable improvements in treatment strategies, as resistance to most currently available agents is not uncommon. In this study, data on drug resistance in MM were analyzed and led to the following conclusions: resistance occurs via intrinsic and extrinsic mechanisms, including intraclonal heterogeneity, drug efflux pumps, alterations of drug targets, the inhibition of apoptosis, increased DNA repair and interactions with the bone marrow (BM) microenvironment, cell adhesion, and the release of soluble factors. Since MM involves the BM, interactions in the MM-BM microenvironment were examined as well, with a focus on the cross-talk between BM stromal cells (BMSCs), adipocytes, osteoclasts, osteoblasts, endothelial cells, and immune cells. Given the complex mechanisms that drive MM, next-generation treatment strategies that avoid drug resistance must target both the neoplastic clone and its non-malignant environment. Possible approaches based on recent evidence include: (i) proteasome and histone deacetylases inhibitors that not only target MM but also act on BMSCs and osteoclasts; (ii) novel peptide drug conjugates that target both the MM malignant clone and angiogenesis to unleash an effective anti-MM immune response. Finally, the role of cancer stem cells in MM is unknown but given their roles in the development of solid and hematological malignancies, cancer relapse, and drug resistance, their identification and description are of paramount importance for MM management.