In a relatively short period of chromosome replication issues were the focus of oncologists. At the end of each chromosome are repeated hexanucleotide sequences called telomeres. In connection with certain limitations chromosomal replication, with each cell division, there is a gradual telomere shortening. This process is sometimes compared to clock elapsed time living mitotic cells. Too short telomeres are a signal informing about aging and are recognized by sophisticated mechanisms as a necessary pause a moment subdivisions. Cancer cells that are able to bypass this step, exceed the threshold of immortality. This article describes the mechanisms responsible for the replication of telomeres, allowing unlimited proliferation of tumor cells, and diagnostic and therapeutic perspectives associated with it.