Just over 125 years has passed since the ‘filterable’ agents of tobacco mosaic disease and foot-and-mouth disease were first described as infectious, replicating entities smaller than bacteria. Today, viruses are formally classified into more than 16,000 species ranked into genera, families and higher taxa. The development of an official virus taxonomy has been overseen by an International Committee, first constituted in 1966 and renamed as the International Committee on Taxonomy of Viruses (ICTV) in 1975. Despite the engagement of the ICTV in virus taxonomy over the last 60 years, many aspects of virus classification and nomenclature may seem odd or sometimes incomprehensible to virologists more familiar with the taxonomy of cellular organisms. Who runs the ICTV? What are virus species demarcation criteria? Why have all virus species names become binomial? How can a sequence in a metagenomic dataset be assigned to a virus species? This article attempts to answer several such questions and outlines how a large, inclusive and global community of virologists has developed new and responsive policies for virus taxonomy in a decade when the pace of virus discovery has dramatically accelerated.