Ten years after the identification of the first partial sequences of Torque teno virus (TTV), more than 200 full-length related genomes have been characterized in humans and in several animal species. As suspected in the earlier stages of their description, a considerable genetic variability characterizes TTV and related viruses, the current members of the floating genus Anellovirous. Since information related to anelloviruses diversity is in constant evolution, the challenge in their taxonomic classification is to take into account all pertinent parameters, along with the taxonomic situation of other viruses having circular single-stranded DNA genomes. Past, present and future phylogenetic and taxonomic considerations are exposed.