An apostolic see is an episcopal see whose foundation is attributed to one or more of the apostles of Jesus or to one of their close associates. In Catholicism the phrase, preceded by the definite article and usually capitalized, refers to the See of Rome.  
Tertullian (c. 155 − c. 240) gives examples of apostolic sees: he describes as churches "in which the very thrones of the apostles are still pre-eminent in their places, in which their own authentic writings are read, uttering the voice and representing the face of each of them severally" the following churches: Corinth, Philippi, Ephesus, and Rome. 
Tertullian says that from these "all the other churches, one after another, derived the tradition of the faith, and the seeds of doctrine, and are every day deriving them, that they may become churches. Indeed, it is on this account only that they will be able to deem themselves apostolic, as being the offspring of apostolic churches". 
Tertullian himself and the slightly earlier Irenaeus (c. 130 – c. 200) speak of the succession of bishops of sees founded directly by the apostles as sources for sure Christian doctrine.
Irenaeus argues that, to know what is true Christian doctrine, it is enough to learn the teaching of some of the oldest churches or at least one, in particular that of Rome:  "If the apostles had known hidden mysteries, which they were in the habit of imparting to 'the perfect' apart and privily from the rest, they would have delivered them especially to those to whom they were also committing the Churches themselves.  [...] Suppose there arise a dispute relative to some important question among us, should we not have recourse to the most ancient Churches with which the apostles held constant intercourse, and learn from them what is certain and clear in regard to the present question?" 
Tertullian's arguing is similar: From the apostles the churches they founded received the doctrine that the apostles received directly from Christ, and from those churches the more recent churches received the same doctrine. Every heresy is more recent and, being different, is erroneous.  
Jurisdictional authority of particular episcopal sees over others is not necessarily associated with the apostolic origin of the see. Thus, the fourth canon of the First Council of Nicaea of 325 attributed to the bishop of the capital (metropolis) of each Roman province (the "metropolitan bishop") a position of authority among the bishops of the province, without reference to the founding figure of that bishop's see. 
Its sixth canon the same council recognized the wider authority, extending beyond a single imperial province, traditionally held by Rome and Alexandria, and the prerogatives of the churches in Antioch and the other provinces. 
Of Aelia, the Roman city built on the site of the destroyed city of Jerusalem, the council's seventh canon reads: "Since custom and ancient tradition have prevailed that the Bishop of Aelia should be honoured, let him, saving its due dignity to the Metropolis, have the next place of honour."  The metropolis in question is generally taken to be Caesarea Maritima,     though in the late 19th century Philip Schaff also mentioned other views. 
The see of Constantinople was elevated to a position of jurisdictional prominence not on the grounds of apostolic origin but because of its political importance as the capital of the Roman Empire. The First Council of Constantinople (381), held in what by then had been the political capital for half a century, decreed in a canon of disputed validity: "The Bishop of Constantinople, however, shall have the prerogative of honour after the Bishop of Rome; because Constantinople is New Rome."  It was later ranked second among the sees in the theory of Pentarchy: "[F]ormulated in the legislation of the emperor Justinian I (527–565), especially in his Novella 131, the theory received formal ecclesiastical sanction at the Council in Trullo (692), which ranked the five sees as Rome, Constantinople, Alexandria, Antioch, and Jerusalem." 
For another pentarchic see, that of Alexandria, the reputed founder and close associate of the apostle Peter, Saint Mark, is not called an apostle in the New Testament.
By a long-standing usage, evidenced already in 431, when the Council of Ephesus, the third ecumenical council, employed the phrase "our most holy and blessed pope Cœlestine, bishop of the Apostolic See",  the expression, "the Apostolic See", is used in the singular and capitalized to mean specifically the see of Rome in reference to the Pope's status as successor of the Apostle Peter.  
In Catholic canon law, the term is applied also to the various departments of the Roman Curia. The Code of Canon Law states: "In this Code the terms Apostolic See or Holy See mean not only the Roman Pontiff, but also, unless the contrary is clear from the nature of things or from the context, the Secretariat of State, the Council for the public affairs of the Church, and the other Institutes of the Roman Curia."  The bodies in question are seen as speaking on behalf of the See of Rome.
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Alphabetical list of Eastern Christianity-related articles on English Wikipedia
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Articles related to Christianity include:
The following outline is provided as an overview of and topical guide to the Catholic Church: