The Nobel Prize in Physiology or Medicine was recently awarded to Elizabeth Blackburn, Carol Greider and Jack Szostak for their pioneering studies on chromosome termini (telomeres) and their discovery of telomerase, the enzyme that synthesizes telomeres. Telomerase is a unique cellular reverse transcriptase that contains an integral RNA subunit, the telomerase RNA and a catalytic protein subunit, the telomerase reverse transcriptase (TERT), as well as several species-specific accessory proteins. Telomerase is essential for genome stability and is associated with a broad spectrum of human diseases including various forms of cancer, bone marrow failure and pulmonary fibrosis. A better understanding of telomerase structure and function will shed important insights into how this enzyme contributes to human disease. To this end, a series of high-resolution structural studies have provided critical information on TERT architecture and may ultimately elucidate novel targets for therapeutic intervention. In this review, we discuss the current knowledge of TERT structure and function, revealed through the detailed analysis of TERT from model organisms. To emphasize the physiological importance of telomeres and telomerase, we also present a general discussion of the human diseases associated with telomerase dysfunction.