Below is a description of some of the major sees.
Apostle: Saint Peter
Current Successor: Pope Benedict XVI
The See of Peter gives the holder the title of Pope and leadership over all Catholic Churches in communion with it (Latin Rite and all the Eastern Rites). Probably the most famous of sees and the one most contested over time. For a while the See of Peter had ultimate political sway over all of Western Europe.
Apostle: Saint Andrew
Current successors: The Eastern Orthodox Ecumenical Patriarch Bartholomew I or the Armenian Orthodox Patriarch Mesrob II Mutafyan.
This one claims to be New Rome and for a while claimed to be above the See of Peter because it became the See of Caesar (capital of the Roman Empire). The Eastern Orthodox patriarch is the "first of equals" of all Eastern Orthodox leaders while the Armenian patriarch is not the leader of the Armenian Church.
This see has suffered under 500 plus years of Turkish rule. The Eastern Orthodox patriarch took orders from the Sultan to break communion with Rome in the late 1400s and by law even today must be a citizen of Turkey. The Armenian Church was not even in Constantinople until the Sultan invited it in during an effort to play Christians against each other.
Apostle: Saint Mark the Evangelist
Current Successors: Coptic Catholic Patriarch Antonios Naguib, Coptic (Oriential) Orthodox Pope Shenouda III of Alexandria, Greek Orthodox Patriarch and Pope of Alexandria and all Africa Theodore II.
A see right now contested with nationalistic overtones. The Coptic Catholic and Coptic Orthodox heads are leaders of their respective church and Coptic Egyptians (not ethnically Arab but native Egyptian) while the Greek Orthodox is Greek.
Apostle: Saint Peter
Current Successors: Maronite Catholic Patriarch Nasrallah Pierre Cardinal Sfeir, Melkite Greek Catholic Patriarch Gregory III Laham, Syrian Catholi Patriarch Ignace Pierre VIII Abdel-Ahad, Eastern Orthodox Ignatius IV, and Syriac (Oriential) Orthodox Ignatius Zakka I Iwas
The first major see made by Peter is also the most fought over. The first three are all in communion with Rome while the Roman Catholic Church even had their own patriarch until the 1950s. Both Orthodox and the Melkite Greek Catholic patriarchs are based in Damascus while the other two Catholics are in Lebanon.
Apostle: Saint James
Current Successors: Latin (Roman Catholic) Patriarch Fouad Twal, Eastern Orthodox Patriarch Theofilos, Armenian Patriarch Torkom Manoogian
The Eastern Orthodox and Latin churches members are mostly Arabs but only the Latin Patriarch has the tradition of having Arab patriarchs while the Eastern Orthodox church is led by Greeks. The Armenian Church is headed and caters to the Armenian expat community. The Armenians has had a presence since the 600s because the Eastern Roman Empire was unable to extinguish the Armenian Church in its hinterlands.
Apostle: Saint Thomas
Current Successors: Chaldean Catholic Patriarch Emmanuel III Delly or Assyrian Church of the East Catholicos Dinkha IV
Both these churches are native to Iraq. The Assyrian Church of the East was once in the majority but a series of great geopolitical "wrong choices" has caused mass migration, conversion, and death. The Chaldean Catholic is headquartered in Baghdad but the Assyrian Church of the East has been forced to relocate to Chicago ever since Iraqi independence.