Chromosome stability relies on an adequate length and complete replication of telomeres, the physical ends of chromosomes. Telomeres are composed of short direct repeat DNA and the associated nucleoprotein complex is essential for providing end-stability. In addition, the so-called end-replication problem of the conventional replication requires that telomeres be elongated by a special mechanism which, in virtually all organisms, is based by a reverse transcriptase, called telomerase. Although, at the conceptual level, telomere functions are highly similar in most organisms, the telomeric nucleoprotein composition appears to diverge significantly, in particular if it is compared between mammalian and budding yeast cells. However, over the last years, the CST complex has emerged as a central hub for telomere replication in most systems. Composed of three proteins, it is related to the highly conserved replication protein A complex, and in all systems studied, it coordinates telomerase-based telomere elongation with lagging-strand DNA synthesis. In budding yeast, the Cdc13 protein of this complex also is essential for telomerase recruitment and this specialisation is accompanied by additional regulatory adaptations. Based on recent results obtained in yeast, here, we review these issues and present an updated telomere replication hypothesis. We speculate that the similarities between systems far outweigh the differences, once we detach ourselves from the historic descriptions of the mechanisms in the various organisms.