Most tumours arise through clonal selection and waves of expansion of a somatic cell that has acquired genetic alterations in essential genes either controlling cell death or cell proliferation. Furthermore, stability of the genome in cancer cells becomes precarious and compromised because several cancer-predisposing mutations affect genes that are responsible for maintaining the integrity and number of chromosomes during cell division. Consequently, the archetypical transformation in tumour cells results in aneuploidy. Indeed, almost all tumour cells display a host of karyotype alterations, showing translocations, gains or losses of entire or large parts of chromosomes. Cancers do not necessarily have a higher mutation rate than normal tissue at the nucleotide level, unless they have gained a mutator phenotype through exposure to environmental stress, but rather exhibit gross chromosomal changes. Therefore, it appears that the main mechanism of tumour progression stems from chromosome instability. Chromosomal instability prevailing in tumour cells arises through several different pathways and is probably controlled by hundreds of genes. Therefore, this review describes the main factors that control chromosome stability through telomere maintenance, mechanisms of cell division, and the mitotic checkpoints that govern centrosome duplication and correct chromosome segregation.