Increasing sequence information indicates that RNA viruses constitute a major fraction of marine virus assemblages. However, only 12 RNA virus species have been described, infecting known host species of marine single-celled eukaryotes. Eight of these use diatoms as hosts, while four are resident in dinoflagellate, raphidophyte, thraustochytrid, or prasinophyte species. Most of these belong to the order Picornavirales, while two are divergent and fall into the families Alvernaviridae and Reoviridae. However, a very recent study has suggested that there is extraordinary diversity in aquatic RNA viromes, describing thousands of viruses, many of which likely use protist hosts. Thus, RNA viruses are expected to play a major ecological role for marine unicellular eukaryotic hosts. In this review, we describe in detail what has to date been discovered concerning viruses with RNA genomes that infect aquatic unicellular eukaryotes.