Telomerase is the enzyme responsible for maintenance of the length of telomeres by addition of guanine-rich repetitive sequences. Telomerase activity is exhibited in gametes and stem and tumor cells. In human somatic cells, proliferation potential is strictly limited and senescence follows approximately 50-70 cell divisions. In most tumor cells, on the contrary, replication potential is unlimited. The key role in this process of the system of the telomere length maintenance with involvement of telomerase is still poorly studied. Undoubtedly, DNA polymerase is not capable of completely copying DNA at the very ends of chromosomes; therefore, approximately 50 nucleotides are lost during each cell cycle, which results in gradual telomere length shortening. Critically short telomeres cause senescence, following crisis and cell death. However, in tumor cells the system of telomere length maintenance is activated. Much work has been done regarding the complex telomere/telomerase as a unique target, highly specific in cancer cells. Telomeres have additional proteins that regulate the binding of telomerase. Telomerase, also associates with a number of proteins forming the sheltering complex having a central role in telomerase activity. This review focuses on the structure and function of the telomere/telomerase complex and its altered behavior leading to disease, mainly cancer. Although telomerase therapeutics are not approved yet for clinical use, we can assume that based on the promising in vitro and in vivo results and successful clinical trials, it can be predicted that telomerase therapeutics will be utilized soon in the combat against malignancies and degenerative diseases. The active search for modulators is justified, because the telomere/telomerase system is an extremely promising target offering possibilities to decrease or increase the viability of the cell for therapeutic purposes.