As US troops complete their withdrawal from Iraq, more than eight years after the invasion that ousted Saddam Hussein, they leave behind a country still facing a litany of challenges.

Here is an overview of some of the key problems:

- Disputed territories:

Iraq's autonomous Kurdish region in the north wants a swathe of territory stretching from the border with Iran to the Syrian frontier to be incorporated into its three-province area.

Baghdad also claims the land, which includes portions of four provinces, and centres around the oil-rich, multi-ethnic city of Kirkuk.

- Insurgents and Al-Qaeda

The Sunni insurgency has dramatically declined since violence peaked in 2006 and 2007, thanks to an alliance between Sunni tribesmen and the US military against Al-Qaeda since late 2006.

Attacks, kidnappings and executions remain common, however, and the Islamic State of Iraq, Al-Qaeda's front group, still carries out major attacks against the security forces, Shiites and Christians.

- Tensions between religious communities

Many Iraqis accuse the US of bringing sectarianism to politics, a dimension they say was largely absent under Saddam. The Shiite-led government has accused Sunni Arabs, who dominated Saddam's regime, of plotting to overthrow it.

On Saturday, the Sunni-backed Iraqiya bloc suspended its participation in parliament over what it claimed was Prime Minister Nuri al-Maliki's centralisation of decision-making power.

- Syria crisis

Iraq shares a long border with Syria, where an offshoot of Saddam's Baath Party rules. A potential fall of Syria's minority Shiite Alawite regime could push refugees across the frontier, threatening to raise tensions between Iraqi Sunnis and Shiites.

- Iranian influence

Iran is widely believed to exert major influence on the government, and has been accused by Washington of training and equipping Shiite militias in the south of Iraq, charges Tehran denies.

- Institutional corruption and fragility

Iraq lacks an interior minister, and no permanent defence minister has been named since March 2010 elections because of political disputes.

Institutions are weak and rife with graft, with Iraq rated the eighth-most corrupt country in the world by Transparency International.

Some provinces want more autonomy, along the lines of the Kurdistan region.

The security forces, while largely able to maintain internal security, are unable to defend borders, air space or maritime territory, and will not be fully capable until 2020, according to Iraq's top military officer.

- Energy

Though oil production and exports, which account for the vast majority of government income, are rising, no law has yet been approved to regulate the industry and the dispersal of revenues between the central government and its provinces.

- Social problems

Nearly a quarter of Iraq's population lives in poverty. The status of women in society has deteriorated markedly since 2003. Iraq also has about 1.75 million refugees and internally displaced persons.

- Kurdish separatists

The Kurdistan Workers' Party (PKK) and Party of Free Life of Kurdistan (PJAK), which have fought against the Turkish and Iranian governments respectively for decades, maintain rear bases in north Iraq. Ankara and Tehran regularly target those bases in air raids and artillery bombardments.

- Tensions with Kuwait

Relations with neighbouring Kuwait have been strained since Saddam's 1990 invasion of the oil-rich emirate, with Iraq frequently complaining about ongoing reparations and the still-incomplete demaraction of the border.

Baghdad also accuses Kuwait of blocking its maritime access, and thereby threatening its oil exports, by constructing a massive port.

Key dates in Iraq since US invasion
Baghdad (AFP) Dec 18, 2011 - US troops left Iraq and crossed into neighbouring Kuwait on Sunday, completing their withdrawal from the country and ending an almost nine-year campaign.

Here are some key dates in the American presence in Iraq:

2003

March 20: US-led forces begin onslaught against Iraq, which they accuse of harbouring weapons of mass destruction.

April 9: US forces topple a large statue of Saddam Hussein in Baghdad.

May 1: US President George W. Bush announces the end of major combat operations using a "Mission Accomplished" banner.

October 2: US admits no weapons of mass destruction found.

October 16: UN Resolution 1511 legitimises the US-led occupation.

December 13: Saddam captured.

2004

April-August: Clashes between coalition forces and militiamen of Shiite radical leader Moqtada al-Sadr.

April 28: Photographs emerge of US forces humiliating inmates at Abu Ghraib prison.

June 28: The US-led administration hands Iraqis power.

2005

January 30: Iraqis vote in the first multi-party poll in 50 years despite deadly attacks, a poll Sunni Arabs largely boycott.

April 6-7: Jalal Talabani becomes president, the first Kurd in the post. Ibrahim al-Jaafari, a Shiite, becomes prime minister.

December 15: The conservative Shiite United Iraqi Alliance wins most seats in parliamentary elections.

2006

February 22: Revered Shiite shrine in Samarra blown up; sectarian unrest kills 450 people.

May 20: New Prime Minister Nuri al-Maliki formally presents cabinet to parliament for approval.

June 7: US air strike kills Al-Qaeda in Iraq leader Abu Musab al-Zarqawi.

July: The US hands over to Iraq's security control of 18 provinces.

December 30: Saddam hanged.

2007

January 10: Bush deploys 30,000 more troops in a so-called "surge" strategy.

2008

March 23: 4,000 US soldiers dead in Iraq since invasion.

November 27: Parliament ratifies a security agreement setting the framework for a US troop presence beyond the end of the year.

2009

January 1: The US transfers control of Baghdad's high-security Green Zone.

February 27: President Barack Obama sets August 31, 2010 deadline for end to US combat operations, with a total retreat by end 2011.

June 30: US forces quit urban areas.

August 19, October 25, December 8: At least 386 are killed in attacks on government buildings in Iraq.

2010

January 1: US troops rename their force "United States Forces-Iraq," from "Multi-National Forces-Iraq," after all other countries pull soldiers out.

March 7: Inconclusive second parliamentary elections unleash political crisis.

August 31: End to US combat operations, with US troops now tasked with training Iraqi forces.

November 10: Iraq's political factions seal a power-sharing deal including all sides.

December 21: Parliament gives Prime Minister Nuri al-Maliki's government a vote of confidence.

2011

August 3: Iraq gives the green light to talks with Washington over a military training mission. Talks later break down.

August 15: At least 74 people are killed in nationwide attacks across 17 cities, claimed for the most part by Al-Qaeda in Iraq.

October 21: Obama announces that US forces, numbering around 39,000, would be withdrawn by the end of the year, after a nearly nine-year campaign and 4,400 American fatalities.

November 9 - December 7: US forces hand Joint Base Balad, north of Baghdad, the Al-Assad air base in the western Anbar province, and the Victory Base Complex near Baghdad over to Iraqi control.

December 11: Prime Minister Nuri al-Maliki travels to Washington, looking to open a new chapter with the United States after the protracted war left deep wounds.

December 15: US forces in Iraq hold a "casing of the colours" ceremony, marking a formal end to their mission in the country.

December 18: The last US troops cross into Kuwait from Iraq, completing the withdrawal. Just 157 soldiers, assigned with training Iraqi forces, remain at the US embassy, along with a small contingent of Marines responsible for the diplomatic mission's security.