Can you tell me why the Catholic Church is based in Rome?  How did the Vatican end up there?

Rome has figured prominently in the history of the Church from its earliest days. Its Jewish community had close ties to Jerusalem, and thus Christianity reached Rome even before Paul came there as a missionary in 49-50. Peter and Paul both met martyrdom in Rome, giving the Christian community there special status. Also, Rome was one of the major cities of the empire; its great concentration of political and economic power proved a significant advantage as the Church grew.

Rome was one of five primary episcopal sees in the early centuries of the Church (along with the other major cities of the empire: Constantinople, Antioch, Jerusalem and Alexandria). But in time the bishop of Rome, seen as the successor to St. Peter, came to be understood as the first among equals. Over the course of 2000 years of history the Church acquired great temporal power and then lost it; the Vatican City is all that remains of once-vast territories under papal control. But the bishop of Rome, the pope, retains primacy today over the Roman Catholic Church which, because of history and tradition, remains based in Rome.