Linear DNA genomes are sporadically found among viruses, bacteria and organelles. In contrast, virtually all eukaryotic species harbor in their nuclei chromosomes consisting of linear DNA molecules that terminate with specific structures termed telomeres, indicat­ ing that this genomic or chromosomal form may, under specific conditions, provide a selective advantage. As the molecular form of eukaryotic chromosomes and their telomeric structures does not seem to be related to any linear genome known in free living prokaryotes, linear chromosomes in eukaryotic nuclei may represent evolutionary innovation. This raises the question of how linear chromosomes and primordial pathways for the maintenance of their terminal structures emerged in eukaryotes. In this chapter we review what we have learned from studies on linear DNA ge­ nomes and their terminal structures in yeast mitochondria. We briefly outline how linear DNA genomes might have emerged in organelles and, based on parallels between the mitochondrial and nuclear systems, suggest a scenario for emergence of linear chromosomes in the nuclei of early eukaryotes.