Centrosome anomalies are detected in virtually all human cancers. They have been implicated in multipolar mitoses, chromosome missegregation, and genomic instability. Despite extensive studies on the type and frequency of centrosome anomalies, a causative relationship between centrosome aberrations and chromosomal instability has been difficult to establish. For example, centrosome amplification can be present without associated chromosomal instability. In addition, not all cells appear to be permissive for centrosome‐related mitotic defects suggesting that cellular mechanisms that limit the harmful effects of spindle malformation on genome integrity may exist. This review proposes to classify centrosome abnormalities in tumor cells into three groups based on their relevance to genomic instability: primary centrosome overduplication, transient centrosome accumulation, and permanent centrosome accumulation. Whereas the first two categories are associated with an increased risk of chromosomal missegregation, the latter category may not contribute to the propagation of genomic instability. Therefore, centrosome anomalies should not per se be viewed as a universal cause of chromosomal instability, rather, they need to be assessed in the cellular context in which they occur.