Apostolic succession is the method whereby the ministry of the Christian Church is held to be derived from the apostles by a continuous succession, which has usually been associated with a claim that the succession is through a series of bishops. Christians of the Roman Catholic, Eastern Orthodox, Oriental Orthodox, Old Catholic, Moravian, Hussite, Anglican, Church of the East, and Scandinavian Lutheran traditions maintain that "a bishop cannot have regular or valid orders unless he has been consecrated in this apostolic succession". These traditions do not always consider the episcopal consecrations of all of the other traditions as valid.

This series was seen originally as that of the bishops of a particular see founded by one or more of the apostles. According to historian Justo L. González, apostolic succession is generally understood today as meaning a series of bishops, regardless of see, each consecrated by other bishops, themselves consecrated similarly in a succession going back to the apostles. According to the Joint International Commission for Theological Dialogue Between the Catholic Church and the Orthodox Church, "apostolic succession" means more than a mere transmission of powers. It is succession in a church which witnesses to the apostolic faith, in communion with the other churches, witnesses of the same apostolic faith. The "see (cathedra) plays an important role in inserting the bishop into the heart of ecclesial apostolicity", but, once ordained, the bishop becomes in his church the guarantor of apostolicity and becomes a successor of the apostles.

Those who hold for the importance of apostolic succession via episcopal laying on of hands appeal to the New Testament, which, they say, implies a personal apostolic succession (from Paul to Timothy and Titus, for example). They appeal as well to other documents of the early Church, especially the Epistle of Clement. In this context, Clement explicitly states that the apostles appointed bishops as successors and directed that these bishops should in turn appoint their own successors; given this, such leaders of the Church were not to be removed without cause and not in this way. Further, proponents of the necessity of the personal apostolic succession of bishops within the Church point to the universal practice of the undivided early Church (up to AD 431), before it was divided into the Church of the East, Oriental Orthodoxy, the Eastern Orthodox Church and the Roman Catholic Church.

Some Protestants deny the need for this type of continuity, and the historical claims involved have been severely questioned by them; Anglican academic Eric G. Jay comments that the account given of the emergence of the episcopate in Chapter III of the dogmatic constitution Lumen gentium (1964) "is very sketchy, and many ambiguities in the early history of the Christian ministry are passed over".