Over 60 years ago Barbara McClintock described the telomere and suggested that it protected the chromosome from illegitimate or end-to-end fusion, thus functioning to protect the genome. Since that time we have discovered that the telomere is a complex structure composed of both DNA and a growing list of associated proteins that together serve to regulate the length of the telomere and, as predicted by McClintock, protect genomic integrity. In addition to its protective role, the telomere has also been hypothesized to serve as a molecular clock that tallies the number of cell divisions and limits further divisions at a predetermined point. However, the precise role of telomeres in predicting and limiting cellular lifespan remains a matter of much debate. In this review, we highlight some of the salient points of basic telomere biology and relate them to the current controversies surrounding the role of telomeres and telomerase in cellular senescence.