Pope Alexander IV built this famous palace, where he and several subsequent Popes chose to reside. It was here that, after the death of Pope Clement IV in 1268 the cardinals gathered to elect the next Pope. When, after 33 months, they still couldn't agree upon the election, the upset Viterbese decided to lock them in the hall of the election, breaking the roof open so as to leave them exposed to the weather, and feeding them with bread and water until they would make a choice. In a short time the Cardinals elected Pope Gregory X: the Papal Conclave tradition was born, setting up the rule of isolation of the cardinals by Gregory X in the Second Council of Lyon in 1274.
However Viterbo, also called the city of the Popes, only saw six Conclaves, as on the last of these in 1280 Charles of Anjou intervened arresting the two most prominent Italian cardinals who were preventing the election of French Pope Martin IV - who moved on to nearby Orvieto with the papal court after being elected.
More info and virtual tour of Viterbo.