Multiple myeloma (MM) is an incurable plasma cell malignancy characterized by genomic instability. MM cells present various forms of genetic instability, including chromosomal instability, microsatellite instability, and base-pair alterations, as well as changes in chromosome number. The tumor microenvironment and an abnormal DNA repair function affect genetic instability in this disease. In addition, states of the tumor microenvironment itself, such as inflammation and hypoxia, influence the DNA damage response, which includes DNA repair mechanisms, cell cycle checkpoints, and apoptotic pathways. Unrepaired DNA damage in tumor cells has been shown to exacerbate genomic instability and aberrant features that enable MM progression and drug resistance. This review provides an overview of the DNA repair pathways, with a special focus on their function in MM, and discusses the role of the tumor microenvironment in governing DNA repair mechanisms.