The genus Sobemovirus, unassigned to any family, consists of viruses with single-stranded plus-oriented single-component RNA genomes and small icosahedral particles. Currently, 14 species within the genus have been recognized by the International Committee on Taxonomy of Viruses (ICTV) but several new species are to be recognized in the near future. Sobemovirus genomes are compact with a conserved structure of open reading frames and with short untranslated regions. Several sobemoviruses are important pathogens. Moreover, over the last decade sobemoviruses have become important model systems to study plant virus evolution. In the current review we give an overview of the structure and expression of sobemovirus genomes, processing and functions of individual proteins, particle structure, pathology and phylogenesis of sobemoviruses as well as of satellite RNAs present together with these viruses. Based on a phylogenetic analysis we propose that a new family Sobemoviridae should be recognized including the genera Sobemovirus and Polemovirus. Finally, we outline the future perspectives and needs for the research focusing on sobemoviruses.