Most cancer genomes show abnormalities in chromosome structure and number, two types of aberrations that could share a common mechanistic origin through proliferation-dependent loss of telomere function. Impairment of checkpoints that limit cell proliferation when telomeres are critically short might allow unrestrained cell division. The resulting uncapped chromosomes can fuse to each other, forming unstable configurations that can bridge during mitosis. Chromatin bridges can break to generate new broken ends that will then fuse with other broken ends. Successive events of break and fusion will continuously generate unbalanced chromosomal rearrangements, leading to gene-copy gains and losses. However, chromosome bridges do not always break. Evidence has recently been obtained to suggest that telomere-dependent chromosome bridges remaining unbroken can hinder cytokinesis and yield tetraploid cells. This might constitute an unstable intermediate in tumorigenesis, as progressive losses of individual chromosomes due to geometrical defects during cell division result in subtetraploid karyotypes. Additionally, the presence of short dysfunctional telomeres in cells can also cause these cells to become sensitive to mutagens, and particularly to radiation exposure. Human individuals exhibit differences in their sensitivity to radiation, which can be relevant for choice of therapy. Telomere function may well be involved in cellular and organism responses to ionizing radiation. Since eroded telomeres are sensed and act as double-strand breaks, they can interact with radiation-induced breaks, sharply increasing the possibility of misjoining. Altogether, this scenario provides certain clues to understanding the important role of telomeres in maintaining genomic integrity.