Due to cell-cycle dysregulation, many cancer cells contain more than the normal compliment of centrosomes, a state referred to as centrosome amplification (CA). CA can drive oncogenic phenotypes and indeed can cause cancer in flies and mammals. However, cells have to actively manage CA, often by centrosome clustering, in order to divide. Thus, CA is also an Achilles' Heel of cancer cells. In recent years, there have been many important studies identifying proteins required for the management of CA and it has been demonstrated that disruption of some of these proteins can cause cancer-specific inhibition of cell growth. For certain targets therapeutically relevant interventions are being investigated, for example, small molecule inhibitors, although none are yet in clinical trials. As the field is now poised to move towards clinically relevant interventions, it is opportune to summarise the key work in targeting CA thus far, with particular emphasis on recent developments where small molecule or other strategies have been proposed. We also highlight the relatively unexplored paradigm of reversing CA, and thus its oncogenic effects, for therapeutic gain.