Telomeres are specialized DNA protein structures that form the ends of eukaryotic chromosomes. In yeast, loss of even a single telomere causes a prolonged, but transitory, cell-cycle arrest. During this arrest, many broken chromosomes acquire a new telomere by one of three pathways, although at the cost of a partial loss of heterozygosity. In addition, a substantial fraction of the chromosomes lacking a telomere is lost, which generates an aneuploid cell. In these cases, the broken chromosome is usually replicated and segregated for ten or more cell divisions in unstable form. Extrapolation from yeast suggests that the gradual loss of telomeric DNA that accompanies ageing in humans may initiate the kinds of chromosomal rearrangements and genetic changes that are associated with tumorigenesis.