Tywin was rewarded handsomely for his decision to turn on the Targaryens. His daughter Cersei was married to the new king, Robert Baratheon, becoming Queen of Westeros and cementing Lannister control over the entire kingdom.
Robert Baratheon was, however, much more of a fighter than a leader. His time on the throne was marked by rampant spending on feasts, fun, and the occasional small-scale war, nearly all of it financed by the Lannisters. Because of the extreme debt the crown owed the Lannisters, the family became regarded as the realm's true reigning house, and Tywin Lannister as one of its most powerful figures.
Cersei gave Robert several heirs in Joffrey, Tommen and Myrcella. Though they all carried the Baratheon name,their striking blond hair fueled (entirely true) gossip that they were, in fact, fathered by Jaime, and therefore had no claim to the throne. This quickly became an issue when Robert died from wounds sustained on a hunting trip and the young, cruel Joffrey ascended to the throne.
