Viruses are extremely diverse and not all of this diversity has been captured so far. In this Review, Martinez Martinez, Martinez-Hernandez and Martinez-Garcia explore the potential and limitations of single-virus genomics and how this emerging technology can complement other methods. Viruses are extremely diverse and modulate important biological and ecological processes globally. However, much of viral diversity remains uncultured and yet to be discovered. Several powerful culture-independent tools, in particular metagenomics, have substantially advanced virus discovery. Among those tools is single-virus genomics, which yields sequenced reference genomes from individual sorted virus particles without the need for cultivation. This new method complements virus culturing and metagenomic approaches and its advantages include targeted investigation of specific virus groups and investigation of genomic microdiversity within viral populations. In this Review, we provide a brief history of single-virus genomics, outline how this emergent method has facilitated advances in virus ecology and discuss its current limitations and future potential. Finally, we address how this method may synergistically intersect with other single-virus and single-cell approaches.