The Catholic Church affirms Matthew 16:18 as establishing Peter as the 'rock' (Gk. petra; Lat. petrus) upon which Christ builds His Church, and interprets this as the foundation for papal primacy and episcopal succession. The First Council of the Vatican (1870) defined papal infallibility in matters of faith and morals when speaking ex cathedra, and this doctrine is grounded in Catholic exegesis of Matthew 16:18-19. The Catechism of the Catholic Church (§§ 880-887) presents the Pope as the successor of Peter and holder of the keys of the kingdom.

Catholic theology understands the gift of the keys and the binding and loosing authority as conferring legislative, judicial, and pastoral authority to Peter and his successors. This reading is supported by parallel passages (Matthew 18:18, John 21:15-17) where similar authority is transmitted to the apostolic community. The doctrine of papal primacy has been developed throughout Catholic tradition, from Augustine through Thomas Aquinas to modern papal documents, and rests on this Matthean foundation.