Multiple myeloma (MM) is a complex hematological malignancy characterized by abnormal proliferation of malignant plasma cells (PCs) within a permissive bone marrow microenvironment. The pathogenesis of MM is unequivocally linked to the acquisition of genomic instability (GI), which indicates the tendency of tumor cells to accumulate a wide repertoire of genetic alterations. Such alterations can even be detected at the premalignant stages of monoclonal gammopathy of undetermined significance (MGUS) and smoldering multiple myeloma (SMM) and, overall, contribute to the acquisition of the malignant traits underlying disease progression. The molecular basis of GI remains unclear, with replication stress and deregulation of DNA damage repair pathways representing the most documented mechanisms. The discovery that non-coding RNA molecules are deeply dysregulated in MM and can target pivotal components of GI pathways has introduced a further layer of complexity to the GI scenario in this disease. In this review, we will summarize available information on the molecular determinants of GI in MM, focusing on the role of non-coding RNAs as novel means to tackle GI for therapeutic intervention.