Satellite viruses encode structural proteins required for the formation of infectious particles but depend on helper viruses for completing their replication cycles. Because of this unique property, satellite viruses that infect plants, arthropods, or mammals, as well as the more recently discovered satellite-like viruses that infect protists (virophages), have been grouped with other, so-called "sub-viral agents." For the most part, satellite viruses are therefore not classified. We argue that possession of a coat-protein-encoding gene and the ability to form virions are the defining features of a bona fide virus. Accordingly, all satellite viruses and virophages should be consistently classified within appropriate taxa. We propose to create four new genera - Albetovirus, Aumaivirus, Papanivirus, and Virtovirus - for positive-sense single-stranded (+) RNA satellite viruses that infect plants and the family Sarthroviridae, including the genus Macronovirus, for (+)RNA satellite viruses that infect arthopods. For double-stranded DNA virophages, we propose to establish the family Lavidaviridae, including two genera, Sputnikvirus and Mavirus.