Since 1998, when Jim van Etten’s team initiated its characterization, Paramecium bursaria Chlorella virus 1 (PBCV-1) had been the largest known DNA virus, both in terms of particle size and genome complexity. In 2003, the Acanthamoeba-infecting Mimivirus unexpectedly superseded PBCV-1, opening the era of giant viruses, i.e., with virions large enough to be visible by light microscopy and genomes encoding more proteins than many bacteria. During the following 15 years, the isolation of many Mimivirus relatives has made Mimiviridae one of the largest and most diverse families of eukaryotic viruses, most of which have been isolated from aquatic environments. Metagenomic studies of various ecosystems (including soils) suggest that many more remain to be isolated. As Mimiviridae members are found to infect an increasing range of phytoplankton species, their taxonomic position compared to the traditional Phycodnaviridae (i.e., etymologically “algal viruses”) became a source of confusion in the literature. Following a quick historical review of the key discoveries that established the Mimiviridae family, we describe its current taxonomic structure and propose a set of operational criteria to help in the classification of future isolates.