Torradoviruses are an example of a group of recently discovered plant viruses. The first description of Tomato torrado virus, now the type member of the newly established genus Torradovirus within the family Secoviridae, was published in 2007 and was quickly followed by findings of other torradoviruses, initially all on tomato. Their characterization led to the development of tools that allowed recognition of still other torradoviruses, only very recently found on non-tomato crops, which indicates these viruses have a much wider host range and diversity than previously believed. This review describes the characteristics of this newly emerged group of plant viruses. It looks in detail at taxonomic relationships and specific characteristics in their genomes and encoded proteins. Furthermore, it discusses their epidemiology, including host range, semipersistent transmission by whitefly vectors, and impact on diverse cropping systems.