The very end of the chromosome is called the telomere and is composed of DNA repeat sequences and associated proteins. Genetic and biochemical analyses of this complex, the telosome, lead to the hypothesis that transcription and DNA replication are submitted to position effects mediated by the telomere proximity. Telomere length reduction and alterations of the telomeric chromatin assembly might explain the chromosome instability which occurs during the senescence and the immortalization process in vitro. A particular polymerase, the telomerase, is able to lengthen the telomeres. A telomerase activity was characterized in yeast, Tetrahymena, but also in transformed and in germline cells. We reviewed the involvement of telomeres in the aging process. We proposed that the short size of the telomere repeat at each chromosome could direct the loss of heterozygosity, thus telomere length could play a role in individual and tissular susceptibility to develop cancer. Antitelomerase strategy for cancer therapy is attractive but limited by the short decrease of the telomere length at each cell division.