Proper partitioning of replicated sister chromatids at each mitosis is crucial for maintaining cell homeostasis. Errors in this process lead to aneuploidy, a condition in which daughter cells harbor genome imbalances. Importantly, aneuploid cells often experience DNA damage, which in turn could drive genome instability. This might be the product of DNA damage accumulation in micronuclei and/or a consequence of aneuploidy-induced replication stress in S-phase. Although high levels of genome instability are associated with cell cycle arrest, they can also confer a proliferative advantage in some circumstances and fuel tumor growth. Here, we review the main consequences of chromosome segregation errors on genome stability, with a special focus on the bidirectional relationship between aneuploidy and DNA damage. Also, we discuss recent findings showing how increased genome instability can provide a proliferation improvement under specific conditions, including chemotherapeutic treatments.