Although the species is the fundamental unit of taxonomy, virologists only recently have begun to classify virus species in a systematic way under the leadership of the International Committee on Taxonomy of Viruses. Progress has been slow and uneven for several reasons: (i) Attempts to sort species are hampered even when the distinction between classification and nomenclature is blurred. Classifying is based on observation and involves deductive reasoning, whereas naming can be as arbitrary as desired, even to the point of dispensing with the traditional Latin binomial form. (ii) Some virologists deny the possibility of applying the species concept to asexual organisms, such as viruses. Those persons are influenced by an obsolete definition of biological species which rests on observed or inferred barriers to sexual reproduction. (iii) New taxonomic tools, such as mathematical (numerical) taxonomy, might be applied profitably to virus classification, but are unfamiliar to many virologists.