The war in Iraq did not play out quite like the mass media portrayed it. The one thing there is most agreement on is that nearly all the violence was the result of terror attacks on Shia and Sunni Arab civilians. This violence peaked in late 2006-early 2007, during which time civilian deaths were at least 3,000 a month. They have greatly declined since then, with December 2010 being the lowest, with 151 civilian deaths.
The war was concentrated in Baghdad, and later other areas where Sunni Arab terrorists sought to make a stand. Baghdad was the major battlefield partly because it was the national capital, and a city of great historical significance in Islamic history, and mostly because it's where the Sunni Arab upper class, and many oppressed Shia Arabs lived. While Sunni Arab terrorists attacked Shia shrines in the south, the Baghdad Shia organized their own death squads and drove most of the Sunni Arabs out of Baghdad.
These attacks on civilian populations decided the war. The Sunni Arabs, starting out as 20 percent of the population, ended up as 15 percent, with most Sunni Arabs driven from their homes (and many out of the country.) After 2007, the remaining violence shifted north, where Sunni Arabs lived next to Kurds. Many of those Sunni Arabs had been moved into former Kurdish farms and homes, after Saddam had the Kurds driven farther north in the 1980s and 90s. The Kurds wanted their property back.
While the Kurds were also a minority (about 15 percent of the population), they had gained autonomy in the early 1990s when the U.S. and Britain used air power to keep Iraqi police and troops out of the Kurdish north. The Kurds proceeded to form a security force that spared the Kurdish north all but a few terror attacks after 2003. The same pattern developed in the south, even though much of the southwest was occupied by Sunni Arab tribes (living alongside Shia Arab tribes.) The Sunni Arabs in the south quickly made their peace with the Shia majority, and for nearly all the war (2003-7), the south was quiet.
The only other battlefield was western Iraq (Anbar Province) which was thinly populated, almost entirely by Sunni Arab tribes. It was a battlefield mainly because American and Iraqi forces kept fighting the Sunni Arab terrorists there. Eventually, most of the Sunni Arab tribes joined the government, as they also did in Baghdad, and most of the fighting was over,
Since 2007, violence has declined 90 percent. There is still violence in the north (where Kurds and Arabs battle over control of oil fields), and in Baghdad (where Sunni Arabs kill for media attention). But as wars go, this one is over, that is how it went.