Discusses telomeres, complexes of DNA and protein that form the chromatin at the ends of chromosomes. Highlights telomeres as controllers of chromosome integrity, expendable telomeres, DNA replication requirements and their consequences, protection of structural genes, telomerase as indicators of immortality, cancer cells and other immortals, and intriguing questions concerning telomeres and telomerase that remain unanswered. Contains 36 references. (JRH)