In virtually every eukaryotic species, the ends of nuclear chromosomes are protected by telomeres, nucleoprotein structures counteracting the end-replication problem and suppressing recombination and undue DNA repair. Although in most cases, the primary structure of telomeric DNA is conserved, there are several exceptions to this rule. One is represented by the telomeric repeats of ascomycetous yeasts, which encompass a great variety of sequences, whose evolutionary origin has been puzzling for several decades. At present, the key questions concerning the driving force behind their rapid evolution and the means of co-evolution of telomeric repeats and telomere-binding proteins remain largely unanswered. Previously published studies addressed mostly the general concepts of the evolutionary origin of telomeres, key properties of telomeric proteins as well as the molecular mechanisms of telomere maintenance; however, the evolutionary process itself has not been analyzed thoroughly. Here, we aimed to inspect the evolution of telomeres in ascomycetous yeasts from the subphyla Saccharomycotina and Taphrinomycotina, with special focus on the evolutionary origin of species-specific telomeric repeats. We analyzed the sequences of telomeric repeats from 204 yeast species classified into 20 families and as a result, we propose a step-by-step model, which integrates the diversity of telomeric repeats, telomerase RNAs, telomere-binding protein complexes and explains a propensity of certain species to generate the repeat heterogeneity within a single telomeric array.