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 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 In 2003, The Acanthamoeba-infecting Mimivirus unexpectedly superseded PBCV-1, opening the era of giant viruses, i.e. with virions large enough to be visible by light microscopy and genomes encoding more proteins than many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 15 following years, the isolation of many Mimivirus-relatives, have made the Mimiviridae one of the largest and most diverse family of eukaryotic viruses isolated from aquatic environments. Metagenomic studies keep suggesting that many more remain to be isolated. As Mimiviridae members are found to infect an increasing range of phytoplanckton species, their taxonomic position compared to the traditional Phycodnaviridae (i.e. etymologically “algal viruses”) became a source of confusion in the literature. Following a rapid history 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.