The family Circoviridae contains viruses with covalently closed, circular, single-stranded DNA (ssDNA) genomes, including the smallest known autonomously replicating, capsid-encoding animal pathogens. Members of this family are known to cause fatal diseases in birds and pigs and have been historically classified in one of two genera: Circovirus, which contains avian and porcine pathogens, and Gyrovirus, which includes a single species (Chicken anemia virus). However, over the course of the past six years, viral metagenomic approaches as well as degenerate PCR detection in unconventional hosts and environmental samples have elucidated a broader host range, including fish, a diversity of mammals, and invertebrates, for members of the family Circoviridae. Notably, these methods have uncovered a distinct group of viruses that are closely related to members of the genus Circovirus and comprise a new genus, Cyclovirus. The discovery of new viruses and a re-evaluation of genomic features that characterize members of the Circoviridae prompted a revision of the classification criteria used for this family of animal viruses. Here we provide details on an updated Circoviridae taxonomy ratified by the International Committee on the Taxonomy of Viruses in 2016, which establishes the genus Cyclovirus and reassigns the genus Gyrovirus to the family Anelloviridae, a separate lineage of animal viruses that also contains circular ssDNA genomes. In addition, we provide a new species demarcation threshold of 80% genome-wide pairwise identity for members of the family Circoviridae, based on pairwise identity distribution analysis, and list guidelines to distinguish between members of this family and other eukaryotic viruses with circular, ssDNA genomes.