In episcopal churches, the Apostolic Succession is understood to be the basis of the authority of bishops (the episcopate). Specifically in the case of the Catholic Church, the Apostolic Succession as passed on through Saint Peter is also the basis for the specific claim of papal primacy. Within the Anglican Communion this is seen more as a symbolic precedence, not unlike the Eastern Orthodox Patriarch of Constantinople. In any event, all these communions recognize Apostolic Succession as the determining criterion of a particular group's legitimacy as a catholic Church.
Catholic and Orthodox ChurchesThe Catholic Church (including its rites), Eastern Orthodox, Oriental Orthodox, Assyrian, Independent Catholic, and some others hold that apostolic succession is maintained through the consecration of their bishops in unbroken personal succession back to the apostles. In Catholic and Orthodox theology, the unbrokenness of apostolic succession is significant because of Jesus Christ's promise that the "gates of hell" (Matthew 16:18) would not prevail against the Church, and his promise that he himself would be with the apostles to "the end of the age" (Matthew 28:20). According to this interpretation, a complete disruption or end of such apostolic succession would mean that these promises were not kept as would an apostolic succession which, while formally intact, completely abandoned the teachings of the Apostles and their immediate successors; as, for example, if all the bishops of the world agreed to abrogate the Nicene Creed or to repudiate the Bible.