Polintons (also known as Mavericks) are large DNA transposons that are widespread in the genomes of eukaryotes. We have recently shown that Polintons encode virus capsid proteins, which suggests that these transposons might form virions, at least under some conditions. In this Opinion article, we delineate the evolutionary relationships among bacterial tectiviruses, Polintons, adenoviruses, virophages, large and giant DNA viruses of eukaryotes of the proposed order 'Megavirales', and linear mitochondrial and cytoplasmic plasmids. We hypothesize that Polintons were the first group of eukaryotic double-stranded DNA viruses to evolve from bacteriophages and that they gave rise to most large DNA viruses of eukaryotes and various other selfish genetic elements.