Aneuploidy is a ubiquitous feature of cancer and pre-cancerous lesions, yet its significance is poorly characterized. In this chapter, we review the role of tetraploidy and aneuploidy in progression. We examine how aneuploidy may contribute to the evolutionary dynamics prevalent in neoplastic progression, considering whether aneuploidy itself is selectively neutral or advantageous or if it simply acts as a mechanism for the more rapid accumulation of mutations increasing survival and reproduction of cancer cells. We also review evidence from Barrett's esophagus, a pre-malignant condition, demonstrating that tetraploidy and aneuploidy are correlated with an increased risk of progression to cancer. Ultimately, we aim provide testable hypotheses and methods for understanding the role of aneuploidy in cancer.