Centrosome abnormalities are hallmarks of human cancers. Structural and numerical centrosome abnormalities correlate with tumor aggressiveness and poor prognosis, implicating that centrosome abnormalities could be a cause of tumorigenesis. Since Boveri made his pioneering recognition of the potential causal link between centrosome abnormalities and cancer more than a century ago, there has been significant progress in the field. Here, we review recent advances in the understanding of the causes and consequences of centrosome abnormalities and their connection to cancers. Centrosome abnormalities can drive the initiation and progression of cancers in multiple ways. For example, they can generate chromosome instability through abnormal mitosis, accelerating cancer genome evolution. Remarkably, it is becoming clear that the mechanisms by which centrosome abnormalities promote several steps of tumorigenesis are far beyond what Boveri had initially envisioned. We highlight various cancer-promoting mechanisms exerted by cells with centrosome abnormalities and how these cells possessing oncogenic potential can be monitored.