In Christianity, the concept of an Apostolic Throne refers to one of the historic Patriarchates that was associated with a specific apostle. Saint James the Just is associated with the Apostolic Throne of Jerusalem. Both the Roman Catholic Pope and the Patriarchs of Antioch consider themselves as occupying the Apostolic Throne of St. Peter, as Peter presided over the early church from those locations. The Coptic and Eastern Orthodox Patriarch of Alexandria (also known as the Pope of Alexandria) consider themselves as occupying the throne of St. Mark the Evangelist, who founded the Alexandrian church. The Catholicos of the East of the Assyrian Church of the East and the Ancient Church of the East consider themselves as occupying the apostolic throne of St. Thomas, a view also held by their Syriac Orthodox counterpart, the Maphrian.
Saint John was himself associated with the apostolic throne of Ephesus, although this Apostolic See has been canonically vacant since 1922 (with the current holder of it not recognized by the other Eastern Orthodox churches).
The See of Milan claimed the Apostle Barnabas as its founder, but this was disputed. Nonetheless, this Apostolic Throne was later occupied by the highly important Bishop St. Ambrose, who was the mentor of St. Augustine of Hippo (not to be confused with St. Augustine of Canterbury) presided over the See of Milan, which follows a distinctive rite, the Ambrosian Rite, with a liturgy somewhat different from that of Latin Rite Catholicism.
The Archbishop of Canterbury is crowned atop St. Augustine's Chair, referring to the first holder of that office, St. Augustine of Canterbury, not to be confused with the earlier theologian St. Augustine of Hippo. 
Not all of the apostles are associated with specific "Thrones"; in general, the phrase applies to Apostles that presided over a specific geographic church. Notably, there is no apostolic throne associated with St. Paul, who along with St. Peter was present, at different times, in both Antioch and Rome (where both Peter and Paul were crucified. The phrase is also somewhat interchangeable with "Apostolic See."
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