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I just wanted to add to these excellent comments that the Roman Catholic Church itself variously interpreted Christ's words to the Apostle Peter. for example, Pope St. Gregory I understood the "See of Peter" to include Rome, Antioch (also founded by St Peter) and Alexandria (founded by Peter's assistant St Mark the Evangelist).

When we consider Peter's role in the Church of Jerusalem and the fact that the Church of Constantinople was founded by his brother, St Andrew, then we could also say, with St Gregory I, that the "See of Peter" includes all five original Patriarchates of the Church that exercised such a leadership role, and not just the Church of Rome.

The Western Fathers also considered the See of Rome to have been founded by both Peter and Paul. Rome was the only western City to have been founded by the Apostles, unlike the East that had many, and so Rome became the only (and centralized) Apostolic See in the West. The word "Catholic" means, first and foremost, that the "whole" is present in the "part" as the whole Christ in the Eucharist is present in each small particle.

And every Church from the beginning was headed by its bishop without which there was no Church. That bishop received his authority from Peter and the Apostles directly as did the entire Episcopate. What Peter did in acclaiming Christ as the Son of God, all the other Apostles did as well. In addition, there is a tradition we too become "Peter" spiritually when we assert, with him, that Jesus is the "Christ, the Son of the Living God."

The papal claim of "Vicar of Christ" is actually taken from the role ascribed to the Byzantine Emperor. The papal name of "Pontifex Maximus" is one that is borrowed from the Caesars when they were pagan!

Finally, the Apostles founded Churches, they were never Bishops of Churches themselves. To be a Bishop means that one had to reside in one's See. The Apostles were missionaries who couldn't stay in one place.

So in answer to the question is the Pope the descendant of St Peter? As a Bishop, he is. But so are all other Bishops.

The Pope of Rome was the First among Equals until the schism of A.D. 1054.

The Orthodox Church considers Rome to have separated itself from the Orthodox Church. When reconciliation occurs, the Pope may, once again, assume his place as First among Equals throughout the entire Orthodox Catholic Church of the East, the West, the North and the South!