Multiple myeloma (MM) is an incurable plasma cell malignancy characterized by clonal proliferation of plasma cells and a heterogenous genomic landscape. Copy number and structural changes due to chromosomal instability (CIN) are common features of MM. In this review, we describe how primary and secondary genetic events caused by CIN can contribute to increased instability across the genome of malignant plasma cells; with a focus on specific driver genomic events, and how they interfere with cell-cycle checkpoints, to prompt accelerated proliferation. We also provide insight into other forms of CIN, such as chromothripsis and chromoplexy. We evaluate how the tumor microenvironment can contribute to a further increase in chromosomal instability in myeloma cells. Lastly, we highlight the role of certain mutational signatures in leading to high mutation rate and genome instability in certain MM patients. We suggest that assessing CIN in MM and its precursors states may help improve predicting the risk of progression to symptomatic disease and relapse and identifying future therapeutic targets.