Centrosomes are complex structures, which are embedded into the opposite poles of the mitotic spindle of most animals, acting as microtubule organizing centres. Surprisingly, in several biological systems, such as flies, chicken, or human cells, centrosomes are not essential for cell division. Nonetheless, they ensure faithful chromosome segregation. Moreover, mis-functioning centrosomes can act in a dominant-negative manner, resulting in erroneous mitotic progression. Here, I review the mechanisms by which centrosomes contribute to proper spindle organization and faithful chromosome segregation under physiological conditions and discuss how errors in centrosome function impair transmission of the genomic material in a pathological setting.