The telomeres of most eukaryotes are characterized by guanine-rich repeats synthesized by the reverse transcriptase telomerase. Complete loss of telomerase is tolerated for several generations in most species, but modestly reduced telomerase levels in human beings are implicated in bone marrow failure, pulmonary fibrosis and a spectrum of other diseases including cancer. Differences in telomerase deficiency phenotypes between species most likely reflect a tumour suppressor function of telomeres in long-lived mammals that does not exist as such in short-lived organisms. Another puzzle provided by current observations is that family members with the same genetic defect, haplo-insufficiency for one of the telomerase genes, can present with widely different diseases. Here, the crucial role of telomeres and telomerase in human (stem cell) biology is discussed from a Darwinian perspective. It is proposed that the variable phenotype and penetrance of heritable human telomerase deficiencies result from additional environmental, genetic and stochastic factors or combinations thereof.