The genome sequence is the only characteristic readily obtainable for all known viruses, underlying the growing role of comparative genomics in organizing knowledge about viruses in a systematic evolution-aware way, known as virus taxonomy. Overseen by the International Committee on Taxonomy of Viruses (ICTV), development of virus taxonomy involves taxa demarcation at 15 ranks of a hierarchical classification, often in host-specific manner. Outside the ICTV remit, researchers assess fitting numerous unclassified viruses into the established taxa. They employ different metrics of virus clustering, basing on conserved domain(s), separation of viruses in rooted phylogenetic trees and pair-wise distance space. Computational approaches differ further in respect to methodology, number of ranks considered, sensitivity to uneven virus sampling, and visualization of results. Advancing and using computational tools will be critical for improving taxa demarcation across the virosphere and resolving rank origins in research that may also inform experimental virology.