The practice of classifying organisms into hierarchical groups originated with Aristotle and was codified into nearly immutable biological law by Linnaeus. The heart of taxonomy is the biological species, which forms the foundation for higher levels of classification. Whereas species have long been established among sexual eukaryotes, achieving a meaningful species concept for prokaryotes has been an onerous task and has proven exceedingly difficult for describing viruses and bacteriophages. Moreover, the assembly of viral "species" into higher-order taxonomic groupings has been even more tenuous, since these groupings were based initially on limited numbers of morphological features and more recently on overall genomic similarities. The wealth of nucleotide sequence information that catalyzed a revolution in the taxonomy of free-living organisms necessitates a reevaluation of the concept of viral species, genera, families, and higher levels of classification. Just as microbiologists discarded dubious morphological traits in favor of more accurate molecular yardsticks of evolutionary change, virologists can gain new insight into viral evolution through the rigorous analyses afforded by the molecular phylogenetics of viral genes. For bacteriophages, such dissections of genomic sequences reveal fundamental flaws in the Linnaean paradigm that necessitate a new view of viral evolution, classification, and taxonomy.