The recent discovery of diverse very large viruses, such as the mimivirus, has fostered a profusion of hypotheses positing that these viruses define a new domain of life together with the three cellular ones (Archaea, Bacteria and Eucarya). It has also been speculated that they have played a key role in the origin of eukaryotes as donors of important genes or even as the structures at the origin of the nucleus. Thanks to the increasing availability of genome sequences for these giant viruses, those hypotheses are amenable to testing via comparative genomic and phylogenetic analyses. This task is made very difficult by the high evolutionary rate of viruses, which induces phylogenetic artefacts, such as long branch attraction, when inadequate methods are applied. It can be demonstrated that phylogenetic trees supporting viruses as a fourth domain of life are artefactual. In most cases, the presence of homologues of cellular genes in viruses is best explained by recurrent horizontal gene transfer from cellular hosts to their infecting viruses and not the opposite. Today, there is no solid evidence for the existence of a viral domain of life or for a significant implication of viruses in the origin of the cellular domains.