This paper presents standards and best practices for reporting genome sequences of uncultivated viruses. We present an extension of the Minimum Information about any (x) Sequence (MIxS) standard for reporting sequences of uncultivated virus genomes. Minimum Information about an Uncultivated Virus Genome (MIUViG) standards were developed within the Genomic Standards Consortium framework and include virus origin, genome quality, genome annotation, taxonomic classification, biogeographic distribution and in silico host prediction. Community-wide adoption of MIUViG standards, which complement the Minimum Information about a Single Amplified Genome (MISAG) and Metagenome-Assembled Genome (MIMAG) standards for uncultivated bacteria and archaea, will improve the reporting of uncultivated virus genomes in public databases. In turn, this should enable more robust comparative studies and a systematic exploration of the global virosphere.