Replication of eukaryotic linear chromosomes is incomplete and leaves terminal gaps. The evolutionary widely distributed solution to this "end replication" is twofold: chromosome ends are capped with telomeres, bearing multiple copies of redundant telomeric sequences, and the telomerase enzyme can add (lost) telomeric repeats. Telomerase in humans, as in all mammals, is ubiquitous in all embryonic tissues. In adults, telomerase remains active in germs cells, and, although down-regulated in most somatic tissues, telomerase is active in regenerative tissues and notably, in tumor cells. Telomerase activity is linked to cellular proliferation, and its activation seems to be a mandatory step in carcinogenesis. In contrast to mammals, indeterminately growing multicellular organisms, like fish and crustaceae, maintain unlimited growth potential or 'immortality' in all somatic tissues throughout their entire life. Also this cell immortalization is brought about by maintaining telomerase expression. Disease prognosis for human tumors includes evaluation of cell proliferation, based on the detection of proliferation markers with monoclonal antibodies. The significance of the classical marker Ki-67, and of a novel marker repp-86 are compared with semiquantitative telomerase assays. For tumor therapy, telomerase inhibitors are attractive tools. Results with telomerase knock-out mice have revealed promise, but also risk of this approach. On the other side, telomerase stimulation is attractive for expanding 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, like genuine human monoclonal antibodies.