In the Byzantine Empire, an exarch, from Greek (exarchos), was governor of a province at some remove from the capital Constantinople. The prevailing situation frequently involved him in military operations.
In the Christian Church, an exarch is the deputy of a patriarch, or a bishop who, in Eastern Christendom, holds authority over other bishops, without being a patriarch.
The best-known case is that of the Exarch of Italy, who, after the defeat of the Goths, governed in the name of the Byzantine emperor from Ravenna (552-751) the area of Italy, known as Exarchate of Ravenna, that remained under Byzantine control after the reconquest by Belisarius for Justinian. Ravenna had become the capital of the western Roman Empire in 404 under Honorius. It remained the capital of Italy under the Ostrogoths, and after the reconquest became the seat of the provincial governor (539). Ravenna remained the seat of the Exarch until the revolt of 727 over Iconoclasm. Thereafter, the growing menace of the Lombards and the split between eastern and western Christendom that Iconoclasm caused made the position of the Exarch more and more untenable. The last Exarch was killed by the Lombards in 751.
The Byzantine Exarch of Africa nominally governed also Sardinia and Corsica.
The principle became that, since no addition should be made to the fixed number of five patriarchs of he pentarchy, any bishop with authority over other bishops who was not dependent of any one of these five should be called an exarch. Thus, since the Church of Cyprus was declared autocephalous (at Ephesus in 431), its Primate received the title of Exarch of Cyprus.
The short-lived medieval Churches of Ipek (for Serbia), Achrida (for Bulgaria) and Tirnova (for Romania), were governed by exarchs, though these prelates occasionally took the title of patriarch (Fortescue, Orthodox Eastern Church, 305 sq. 317 sq., 328 sq.). On the same principle the Archbishop of Mount Sinai is an exarch, though in this case, as in that of Cyprus, modern Orthodox usage generally prefers the title "Archbishop".
After imperial Russia destroyed in 1802 the old independent Georgian Church (autocephalous since 750, and whose head was since 1008 styled Catholicos-Patriarchs of Iberia, i.e. the Caucacus), the Primate of Georgia (always a Russian) sat in the Holy Synod at St. Petersburg with the title of Exarch of Georgia (Fortescue, Orthodox Eastern Church, 304-305). On 7 April 1917 the Georgian Patriarchate was restored for the Archbishops of Mtsheta and Tbilisi, with the style Catholicos-Patriarchs of All Georgia; in 1943 its autocephaly was recognized by Russia, and on 3 March 1990 the Georgian Patriarchate was recognized by Constantinople.
After the dismembering of the Ottoman Empire, which like the Byzantine empire had ruled most of Orthodoxy (allowing quite some autonomy under the millet system - see Ethnarch), the pentarchy-number principle, already abandoned in the case of Russia, gave way to the desire of the now politically independent orthodox nations to see their sovereignty reflected in ecclsiastical autonomy - autocephaly - and the symbolic title to crown it: a 'national' Patriarch. There are now about twenty Patriarchs.
In the Eastern Orthodox Church, an Exarch is now a deputy of a Patriarch. In many cases he rules on behalf of the Patriarch a Church outside the home territory of the Patriarchate. Thus, in the United States of America, there are Exarchs representing, among others, the Serbian, Romanian, Bulgarian, and Jerusalem Patriarchs. The style of the Exarchs of the Patriarchate of Jerusalem is "Exarch of the Holy Sepulcher".
The ecclesiastical title of Exarch has disappeared in the Western Catholic Church, being replaced by the terms "Primate" and "Vicar Apostolic".
However, in Eastern Rite Catholic Churches (of Eastern tradition but in full communion with the Bishop of Rome, the Pope), the ecclesiastical title of Exarch is in common use.
These Churches are, in general, not identified with a particular liturgical rite. Thus, no less than fourteen of them use the one same Byzantine Rite, mostly in one or other of only two languages, Greek and Church Slavonic, but they maintain their distinct identities. The use of the word "Rite" (with upper-case R) to refer to these Churches has largely, though not altogether, fallen into disuse and can lead to confusion with the liturgical sense of the word "rite" (see the section about them in the Roman Catholic Church article). Because of population shifts, half or so of these Churches have not just exarchates but full-scale eparchies or even archeparchies outside their original territory.
An Apostolic Exarch is a Bishop of a titular see to whom the Pope, as Bishop of the Roman See of the Apostle Peter, has entrusted the pastoral care of the faithful of an autonomous particular Church in an area, not raised to the rank of eparchy, that is situated outside the home territory of a patriarchate or major archbishopric. An Apostolic Exarch thus corresponds to what in the Latin Rite is called a Vicar Apostolic.
Patriarchs and Major Archbishops may also appoint Exarchs (not always Bishops).
The 2006 Annuario Pontificio listed the following Catholic Exarchates.
Byzantine Empire | Eastern Orthodoxy | Ecclesiastical titles | Gubernatorial titles
Екзарх | Exarch | Exarque | Esarca | Exarchaat | Eksarkki | Exark | Екзарх