Noting a correlation of aneuploidy with tumorigenesis, more than 100 years ago Boveri proposed aneuploidy as a cause of tumorigenesis. Boveri’s hypothesis is now being tested in mice in two ways. First, unattached centromeres are also responsible for the mitotic checkpoint, the major cell cycle control mechanism that acts to maintain diploid chromosome content. Prevention of premature onset of anaphase requires a set of components that act at centromeres to generate a diffusible “wait anaphase” inhibitor. The mitotic checkpoint can be weakened in mice by reduction of CENP-E, a highly processive, centromere-associated kinesin required for stable capture by each centromere of the correct number of spindle microtubules. Reduction in CENP-E produces near diploid aneuploidy from missegregation of whole chromosomes. Second, increased expression of the Plk4 kinase has been used to produce centrosome amplification, thereby generating multipolar spindles that produce more robust chromosome missegregation. Increasing whole chromosomal aneuploidy has revealed that whole chromosomal aneuploidy can act oncogenically, but depending on the preceding genetic damage chromosomal instability can also play a previously unsuspected role in preventing tumorigenesis.