I am not really satisfied with any of the answers given here, because they do not seem to answer the question. First of all _apostolic succession_ refers to the fact that all bishops (that is, all those who have received the fullness of Holy Orders) can trace their Holy Orders all the way back to the Apostles. (See [_Catechism of the Catholic Church_ \[CCC\] 77-79][1]. I will observe that the [_documentation_][2] detailing episcopal consecration only goes back to the Renaissance; however the Catholic Church holds that today’s Holy Orders come from an unbroken line to the Apostles.) Therefore, apostolic succession refers neither to doctrinal orthodoxy, nor to communion with the Bishop of Rome: it refers to the _validity of holy orders_ in a given Church. In addition to its own Holy Orders (both in the Western and the [sui-iuris Eastern Catholic Churches][3]), the Catholic Church recognizes the validity of the Holy Orders (hence of apostolic succession) in the following churches: - All of the Chalcedonian Orthodox Churches, also known as the [Eastern Orthodox Church][4]. - All of the non-Chalcedonian [Oriental Orthodox Churches][5], such as the [Coptic][6], [Ethiopian][7], and [Eretrian][8] Orthodox Churches, as well as the [Armenian Apostolic][9] Churches) - The non-Ephesian Churches (such as the [Assyrian Church of the East][10]). - The [Polish National Catholic Church][11]. (Source: _Wikipedia_ article “[Holy Orders (Catholic Church)][12].”) Notably absent from this list are the members of the [Anglican Communion][13]. As Pope Leo XIII taught in his apostolic letter [Apostolicae Curae][14], the Catholic Church holds that the Anglican Church [lost its ability to consecrate bishops in the 16th Century][15], when it changed its rite for episcopal consecration. (Some individual bishops may have found ways to be ordained validly, but it cannot be affirmed with certainty as a body.) [1]: http://www.vatican.va/archive/ccc_css/archive/catechism/p1s1c2a2.htm [2]: http://www.catholic-hierarchy.org/ [3]: https://en.wikipedia.org/wiki/Eastern_Catholic_Churches [4]: https://en.wikipedia.org/wiki/Eastern_Orthodox_Church [5]: https://en.wikipedia.org/wiki/Oriental_Orthodoxy [6]: https://en.wikipedia.org/wiki/Coptic_Orthodox_Church_of_Alexandria [7]: https://en.wikipedia.org/wiki/Ethiopian_Orthodox_Tewahedo_Church [8]: https://en.wikipedia.org/wiki/Eritrean_Orthodox_Tewahedo_Church [9]: https://en.wikipedia.org/wiki/Armenian_Apostolic_Church [10]: https://en.wikipedia.org/wiki/Assyrian_Church_of_the_East [11]: https://en.wikipedia.org/wiki/Polish_National_Catholic_Church [12]: https://en.wikipedia.org/wiki/Holy_Orders_(Catholic_Church)#Recognition_of_other_churches.27_orders [13]: https://en.wikipedia.org/wiki/Anglican_Communion [14]: https://www.ewtn.com/library/PAPALDOC/L13APCUR.HTM [15]: http://canonlawmadeeasy.com/2011/01/20/the-validity-of-anglican-holy-orders/