Telomeres are DNA and protein structures that form complexes protecting the ends of chromosomes. Understanding of the mechanisms maintaining telomeres and insights into their function have advanced considerably in recent years. This review summarizes the currently known components of the telomere/telomerase functional complex, and focuses on how they act in the control of processes occurring at telomeres. These include processes acting on the telomeric DNA and on telomeric proteins. Key among them are DNA replication and elongation of one telomeric DNA strand by telomerase. In some situations, homologous recombination of telomeric and subtelomeric DNA is induced. All these processes act to replenish or restore telomeres. Conversely, degradative processes that shorten telomeric DNA, and nonhomologous end-joining of telomeric DNA, can lead to loss of telomere function and genomic instability. Hence they too must normally be tightly controlled.