Presented modern taxonomy and nomenclature of the DNA-genomic of viruses of vertebrates animals and humans in accordance with the information ICTV release 2015 (ratification 2016). Described the basic criteria for the classification of viruses: characteristics of the viral genome, the mechanism of replication and virions morphology. Viruses of vertebrates (1120 species) consist of 4 orders, 34 families (12 – DNA-genomic, 22 – RNA-genomic), 11 subfamilies and 219 genera. DNA-genomic viruses of vertebrates (546 species) classified in 1 orders, 12 families, 5 subfamilies and 113 genera. The order Herpesvirales has united family Herpesviridae and Alloherpesviridae. Family Poxviridae, Iridoviridae and Parvoviridae, except of viruses of vertebrates, contain viruses of insects. Described the taxa of viruses:family, subfamily, genera, species. Characterized the basic taxonomic features of DNA-genomic viruses of vertebrates: the shape, size and structure of virions – the presence of outer membrane lipoprotein, capsid symmetry type, the structure of the viral DN and the number of proteins. The attention is focused on the features of reproduction of viruses. The replication of majority DNA-genomic viruses of vertebrates occur in the nucleus of cells, except for members of families Poxviridae and Asfarviridae, which are replicate in the cytoplasm. Yield virions is done due to destruction of cells or budding through the cell membrane (sometimes in combination with exocytosis) depending on the structural organization of the virus.