Bluetongue is a vector-borne virus disease of ruminants that is endemic in tropical and subtropical countries. Since 1998 the virus has also appeared in Europe. Partly due to the seriousness of the disease, bluetongue virus (BTV), a member of genus Orbivirus within the family Reoviridae, has been a subject of intense molecular study for the last three decades and is now one of the best understood viruses at the molecular and structural levels. Viruses of the family Reoviridae, including BTV and other orbiviruses, are characterized primarily by their genome of 10–12 segments of linear, double-stranded RNA (dsRNA). Almost all of these separate segments represent single genes, generating a total of 10–13 virus proteins. The virions are non-lipid-containing icosahedral capsid structures, usually with an outer capsid layer surrounding an inner capsid or core that contains the genome. Shortly after cell entry, this outer capsid is removed to release the inner capsid within which the genome remains sequestered from the cellular triggers of innate immunity. Cores must necessarily, therefore, carry all the transcription machinery of the virus, synthesizing and extruding multiple-capped positive-sense RNAs from each genomic segment into the host cell cytoplasm. Current models for the transcription of the dsRNA genome are based on the polymerase complex contacting the template RNA and the nascent transcript being directed out of the core particle through a pore on its surface. This requires the efficient co-ordination of some half-a-dozen enzyme activities, including helicase, polymerase and RNA capping activity. Considerable advances have been made in recent years in understanding the replicase complexes of these viruses, including BTV. In some cases, 3D structures have complemented this analysis to reveal the fine structural detail of these proteins. The combined activities of the core enzymes produce infectious transcripts necessary and sufficient to initiate BTV infection. Such infectious transcripts can now be synthesized wholly in vitro and, when introduced into cells by transfection, lead to the recovery of infectious virus. Future studies hold the possibility of analysing the consequence of mutation in a replicating virus system.