Telomeres are highly dynamic structures that adjust the cellular response to stress and growth stimulation based on previous cell divisions. This critical function is accomplished by progressive telomere shortening and DNA damage responses activated by chromosome ends without sufficient telomere repeats. Repair of critically short telomeres by telomerase or recombination is limited in most somatic cells, and apoptosis or cellular senescence is triggered when too many uncapped telomeres accumulate. The chance of the latter increases as the average telomere length decreases. The average telomere length is set and maintained in cells of the germ line that typically express high levels of telomerase. In somatic cells, the telomere length typically declines with age, posing a barrier to tumor growth but also contributing to loss of cells with age. Loss of (stem) cells via telomere attrition provides strong selection for abnormal cells in which malignant progression is facilitated by genome instability resulting from uncapped telomeres. The critical role of telomeres in cell proliferation and aging is illustrated in patients with 50% of normal telomerase levels resulting from a mutation in one of the telomerase genes. Here, the role of telomeres and telomerase in human biology is reviewed from a personal historical perspective.