Centrosomes serve as the major microtubule organizing centers in cells and thereby contribute to cell shape, polarity, and motility. Also, centrosomes ensure equal chromosome segregation during mitosis. Centrosome aberrations arise when the centrosome cycle is deregulated, or as a result of cytokinesis failure. A long-standing postulate is that centrosome aberrations are involved in the initiation and progression of cancer. However, this notion has been a subject of controversy because until recently the relationship has been correlative. Recently, it was shown that numerical or structural centrosome aberrations can initiate tumors in certain tissues in mice, as well as invasion. Particularly, we will focus on centrosome amplification and chromosome instability as drivers of intra-tumor heterogeneity and their consequences in cancer. We will also discuss briefly the controversies surrounding this theory to highlight the fact that the role of both centrosome amplification and chromosome instability in cancer is highly context-dependent. Further, we will discuss single-cell sequencing as a novel technique to understand intra-tumor heterogeneity and some therapeutic approaches to target chromosome instability