Multiple Myeloma (MM) is a genetically complex and heterogeneous hematological cancer that remains incurable despite the introduction of novel therapies in the clinic. Sadly, despite efforts spanning several decades, genomic analysis has failed to identify shared genetic aberrations that could be targeted in this disease. Seeking alternative strategies, various efforts have attempted to target and exploit non-oncogene addictions of MM cells, including, for example, proteasome inhibitors. The surprising finding that MM cells present rampant genomic instability has ignited concerted efforts to understand its origin and exploit it for therapeutic purposes. A credible hypothesis, supported by several lines of evidence, suggests that at the root of this phenotype there is intense replicative stress. Here, we review the current understanding of the role of replicative stress in eliciting genomic instability in MM and how MM cells rely on a single protein, Ataxia Telangiectasia-mutated and Rad3-related protein, ATR, to control and survive the ensuing, potentially fatal DNA damage. From this perspective, replicative stress per se represents not only an opportunity for MM cells to increase their evolutionary pool by increasing their genomic heterogeneity, but also a vulnerability that could be leveraged for therapeutic purposes to selectively target MM tumor cells.