Members of this Imperial House ruled as Emperors of the Known Universe from the time of the Butlerian Jihad until the defeat of the 81st Emperor of House Corrino, Padishah Emperor Shaddam IV, by "Muad'dib" (Paul Atreides) and the Fremen approximately 10,000 years later. The Emperor had five daughters, all of them trained as Bene Gesserit (albeit in a somewhat superficially 'courtly' way), but only two play a part in the events of Dune. Wensicia was the mother of Farad'n, the future companion of Ghanima Atreides, and Irulan became the wife (in name only) of Paul Atreides who ousted the Emperor to assume the mantle of power himself.
House Corrino's ancestral planet was Salusa Secundus, the seat of imperial power since the Butlerian Jihad. Due to an atomic aggression by a renegade House, House Corrino and the Golden Lion Throne moved to Kaitain. The offending house is unknown, erased from history.
The harsh conditions of their homeworld encouraged the survival of the strong, and allowed the Corrinos to develop the universe's most-feared military units, the warrior-fanatic Sardaukar, the means by which House Corrino controlled the Empire.
Following their exile to Salusa Secundus after being defeated by Paul Atreides, the Corrinos gradually recovered strength. Farad'n Corrino, grandson of Shaddam IV and last hope for a new Corrino Emperor, made a bid for the throne (spurred on by his mother Princess Wensicia). The proposed return to glory for House Corrino did not succeed.
The remaining Atreides were Leto II and his sister Ghanima. Leto II had been rendered sterile by the sandworm binding process, so to continue the line, Leto II reached an agreement with the Corrino: Farad'n would never rule or marry Ghanima, but he would sire all future heirs to the throne, so all emperors after that point would be half-Atreides, half-Corrino. (Leto married his twin sister Ghanima only in name, for political power.)
Following the death of Leto II 3,500 years later, the Empire of a Million Worlds collapsed in The Scattering. There were no more Corrino Emperors, or Atreides emperors for that matter.
1,500 years after the Scattering, the legendary commander of the armies of the Bene Gesserit was Miles Teg, a descendant of the Ghanima/Farad'n union.
The Legends of Dune prequel trilogy written by Brian Herbert and Kevin J. Anderson - which many fans of the original series consider non-canon - about the Butlerian Jihad give further explanation to the origins of House Corrino.House Corrino originated when Viceroy Faykan Butler, a relative of Serena Butler, managed to combine the titles of Viceroy and Grand Patriarch into one office - his - through much deft political maneuvering. In a speech given immediately after the Battle of Corrin, the final battle of the Jihad, Faykan took much of the credit for the battle (which in fact was mainly organized and carried out by Supreme Bashar Vorian Atreides) and announced that he would change his name to Corrino, to reflect this bit of history.