Kirkuk is a traditionally Kurdish city in northern Iraq, claimed as the center of Kurdish civilization by both the Kurdish Democratic Party and Patriotic Union of Kurdistan. Since it dominates the richest oilfields in Iraq, Saddam Hussein resettled large numbers of Arabs, predominantly Sunni, in the city, so from a pure demographic standpoint, it may no longer be majority Kurd. It is about 250 km north of Baghdad, just outside the northern no-fly zone but still within the semi-autonomous Kurdish areas.
From the archeological standpoint, there are remnants of Kurdish and Turkmen artifacts that may well go back 10,000 years. The Kurds are predominantly Sunni, while the Turkmen are split between Sunni and Shi'a. 
Kirkuk had been just south of the northern no-fly zone protected by Operation NORTHERN WATCH.
Pro-Saddam forces were first fought by irregulars backed by US special operations forces before the war, and then the city was secured by the 173rd Airborne Brigade on April 10, 2003.
Power sharing is complex. Since April 2005, a Kurd, Jalal Talabani, has been the President of Iraq, and also leader of Patriotic Union of Kurdistan Kurdistan President Massoud Barzani supports the U.S. forces and Iraq Prime Minister Nouri al-Malaki's (a Shi'ite) government, the potent PKK (Kurdistan Workers Party), which opposes anything but full Kurdish independence, has fought against al-Malaki and U.S. forces. The PKK also is fighting with Turkey and Iran to create a greater Kurdistan. 
In October 2004 Abdul-Rahman Mustafa, governor of Iraq's northern city of Kirkuk, denied allegations from Turkey and some Turkomen representatives that any attempts have been made to change the demographic character of Kirkuk or to "re-Kurdify" the city after the Arabization program under the former Saddam Hussein regime. Mustafa held to his position that the entire population of Kirkuk should collectively and jointly decide the future of the city -- Kurds, Arabs, Turkomens and Assyrians -- without any outside interference. Mustafa said, "We shall do our best to improve conditions in Kirkuk. If we have not succeeded so far, it is because of lack of sufficient funds and resources. Our aim is to turn Kirkuk into a city of 'brotherhood' among all ethnic and religious groups in the region." 
There have been a series of bombings as U.S. troops withdraw. 437 people died in June. Reuters sees it as a flashpoint between the Shiite-led central government and its supports, and Kurdish nationalists. A single mosque bombing, on the 20th, killed 73.