In 1971 I published a theory in which I first formulated the DNA end replication problem and explained how it could be solved. The solution to this problem also provided an explanation for the Hayflick Limit, which underpins the discovery of in vitro and in vivo cell senescence. I proposed that the length of telomeric DNA, located at the ends of chromosomes consists of repeated sequences, which play a buffer role and should diminish in dividing normal somatic cells at each cell doubling. I also proposed that the loss of sequences containing important information that could occur after buffer loss could cause the onset of cellular senescence. I also suggested that for germline cells and for the cells of vegetatively propagated organisms and immortal cell populations like most cancer cell lines, an enzyme might be activated that would prevent the diminution of DNA termini at each cell division, thus protecting the information containing part of the genome. In the last few years, most of my suggestions have been authenticated by laboratory evidence. the DNA sequences that shorten in dividing normal cells are telomeres and the enzyme that maintains telomere length constant in immortal cell populations is telomerase.