From the Catholic Culture website:
Veneration of the two great Apostles, Peter and Paul, has its roots in the very foundations of the Church. They are the solid rock on which the Church is built. They are at the origin of her faith and will forever remain her protectors and her guides. To them Rome owes her true greatness, for it was under God's providential guidance that they were led to make the capital of the Empire, sanctified by their martyrdom, the center of the Christian world whence should radiate the preaching of the Gospel.
St. Peter suffered martyrdom under Nero, in A.D. 66 or 67. He was buried on the hill of the Vatican where recent excavations have revealed his tomb on the very site of the Basilica of St. Peter's. St. Paul was beheaded in the Via Ostia on the spot where now stands the basilica bearing his name. Down the centuries Christian people in their thousands have gone on pilgrimage to the tombs of these Apostles. In the second and third centuries the Roman Church already stood pre-eminent by reason of her apostolicity, the infallible truth of her teaching and her two great figures, Sts. Peter and Paul.