Multiple myeloma (MM) is a plasma cell malignancy characterized by several genetic abnormalities, including chromosomal translocations, genomic deletions and gains, and point mutations. DNA damage response (DDR) and DNA repair mechanisms are altered in MM to allow for tumor development, progression, and resistance to therapies. Damaged DNA rarely induces an apoptotic response, given the presence of ataxia-telangiectasia mutated (ATM) loss-of-function or mutations, as well as deletions, mutations, or downregulation of tumor protein p53 (TP53) and tumor protein p73 (TP73). Moreover, DNA repair mechanisms are either hyperactive or defective to allow for rapid correction of the damage or permissive survival. Medications used to treat patients with MM can induce DNA damage, by either direct effects (mono-adducts induced by melphalan), or as a result of reactive oxygen species (ROS) production by proteasome inhibitors such as bortezomib. In this review, we will describe the mechanisms of DDR and DNA repair in normal tissues, the contribution of these pathways to MM disease progression and other phenotypes, and the potential therapeutic opportunities for patients with MM.