Centrosomes, the main microtubule-organizing centers in most animal cells, are of crucial importance for the assembly of a bipolar mitotic spindle and subsequent faithful segregation of chromosomes into two daughter cells. Centrosome abnormalities can be found in virtually all cancer types and have been linked to chromosomal instability (CIN) and tumorigenesis. Although our knowledge on centrosome structure, replication, and amplification has greatly increased within recent years, still only very little is known on nature, causes, and consequences of centrosome aberrations in primary tumor tissues. In this review, we summarize our current insights into the mechanistic link between centrosome aberrations, aneuploidy, CIN and tumorigenesis. Mechanisms of induction and cellular consequences of aneuploidy, tetraploidization and CIN, as well as origin and effects of supernumerary centrosomes will be discussed. In addition, animal models for both CIN and centrosome amplification will be outlined. Finally, we describe approaches to exploit centrosome amplification, aneuploidy and CIN for novel and specific anticancer treatment strategies based on the modulation of chromosome missegregation rates.