Multiple myeloma (MM) is the second most common blood cancer. Treatments for MM include corticosteroids, alkylating agents, anthracyclines, proteasome inhibitors, immunomodulatory drugs, histone deacetylase inhibitors and monoclonal antibodies. Survival outcomes have improved substantially due to the introduction of many of these drugs allied with their rational use. Nonetheless, MM patients successively relapse after one or more treatment regimens or become refractory, mostly due to drug resistance. This review focuses on the main drugs used in MM treatment and on causes of drug resistance, including cytogenetic, genetic and epigenetic alterations, abnormal drug transport and metabolism, dysregulation of apoptosis, autophagy activation and other intracellular signaling pathways, the presence of cancer stem cells, and the tumor microenvironment. Furthermore, we highlight the areas that need to be further clarified in an attempt to identify novel therapeutic targets to counteract drug resistance in MM patients.