Replication of linear genomes is incomplete and leaves terminal gaps. Solutions to this 'end replication' problem can be traced back to the prebiotic RNA world: 'fossils' of the presumptive archetypes of telomere structure and of the telomerase enzyme are retained in the terminal structures of some RNA viruses. Telomerase expression in mammals is ubiquitous in embryonic tissues but downregulated in somatic tissues of adults. Exceptions are regenerative tissues and, notably, tumor cells. Telomerase activation is controlled by cellular proliferation, and it is an early step in the development of many tumors. In contrast to mammals, indeterminately growing multicellular organisms, such as fish and crustaceae, maintain telomerase competence in all somatic tissues. In human tumor diagnostics, detection of proliferation markers with monoclonal antibodies is well established, and in this review, the significance of additional telomerase assays is evaluated. Telomerase inhibitors are attractive goals for application in tumor therapy, and telomerase knockout mice have proven that telomere erosion limits the lifespan of cells in vivo. In contrast, telomerase stimulation can be used to expand the potential of cellular proliferation in vitro, with possible applications for transplantation of in vitro expanded human cells, for immortalizing primary human cells as improved tissue models and for the isolation of otherwise intractable products, such as genuine human monoclonal antibodies.