Gross mitotic disturbances are often found in malignant tumours, but not until recently have the molecular causes and the genomic consequences of these abnormalities started to become known. One potential source of mitotic instability is chromosomes with dysfunctional telomeres, giving rise to a high rate of chromatin bridges at anaphase. These bridges could lead either to structural chromosome rearrangements through chromatin fragmentation or to whole-chromosome losses through kinetochore-spindle detachment. Statistical meta-analyses have recently revealed that tumours with high rates of anaphase bridging, such as ovarian, head and neck, and pancreatic carcinomas, are characterised by multimodal distributions of genomic imbalances, consistent with a dramatically increased rate of chromosome rearrangements. In contrast, tumours without gross cell division disturbances are characterised by a monotonously decreasing distribution of genomic changes. This distribution follows a power-law, best described by a preferential attachment model in which the tolerance for chromosomal changes increases steadily with tumour growth. Even though many common cancers, such as breast, colorectal, and renal cell carcinomas adhere to this simple power-law dynamics, the underlying molecular mechanisms remain elusive.