The canonical DNA polymerases involved in the replication of the genome are unable to fully replicate the physical ends of linear chromosomes, called telomeres. Chromosomal termini thus become shortened in each cell cycle. The maintenance of telomeres requires telomerase—a specific RNA-dependent DNA polymerase enzyme complex that carries its own RNA template and adds telomeric repeats to the ends of chromosomes using a reverse transcription mechanism. Both core subunits of telomerase—its catalytic telomerase reverse transcriptase (TERT) subunit and telomerase RNA (TR) component—were identified in quick succession in Tetrahymena more than 30 years ago. Since then, both telomerase subunits have been described in various organisms including yeasts, mammals, birds, reptiles and fish. Despite the fact that telomerase activity in plants was described 25 years ago and the TERT subunit four years later, a genuine plant TR has only recently been identified by our group. In this review, we focus on the structure, composition and function of telomerases. In addition, we discuss the origin and phylogenetic divergence of this unique RNA-dependent DNA polymerase as a witness of early eukaryotic evolution. Specifically, we discuss the latest information regarding the recently discovered TR component in plants, its conservation and its structural features.