The spectrum of viruses in insects is important for subjects as diverse as public health, veterinary medicine, food production, and biodiversity conservation. The traditional interest in vector-borne diseases of humans and livestock has drawn the attention of virus studies to hematophagous insect species. However, these represent only a tiny fraction of the broad diversity of Hexapoda, the most speciose group of animals. Here, we systematically probed the diversity of negative strand RNA viruses in the largest and most representative collection of insect transcriptomes from samples representing all 34 extant orders of Hexapoda and 3 orders of Entognatha, as well as outgroups, altogether representing 1243 species. Based on profile hidden Markov models we detected 488 viral RNA-directed RNA polymerase (RdRp) sequences with similarity to negative strand RNA viruses. These were identified in members of 324 arthropod species. Selection for length, quality, and uniqueness left 234 sequences for analyses, showing similarity to genomes of viruses classified in Bunyavirales (n=86), Articulavirales (n=54), and several orders within Haploviricotina (n=94). Coding-complete genomes or nearly-complete subgenomic assemblies were obtained in 61 cases. Based on phylogenetic topology and the availability of coding complete genomes we estimate that at least 20 novel viral genera in seven families need to be defined, only two of them monospecific. Seven additional viral clades emerge when adding sequences from the present study to formerly monospecific lineages, potentially requiring up to seven additional genera. One long sequence may indicate a novel family. For segmented viruses, cophylogenies between genome segments were generally improved by the inclusion of viruses from the present study, suggesting that in silico misassembly of segmented genomes is rare or absent. Contrary to previous assessments, significant virus-host codivergence was identified in major phylogenetic lineages based on two different approaches of codivergence analysis in a hypotheses testing framework. In spite of these additions to the known spectrum of viruses in insects, we caution that basing taxonomic decisions on genome information alone is challenging due to technical uncertainties, such as the inability to prove integrity of complete genome assemblies of segmented viruses.