More than 6,000 polling stations have opened on time amid tight security in Iraq, where people are voting in a referendum on a new constitution.
Iraqi troops and police, along with US-led foreign forces, have been deployed to try to prevent insurgents disrupting the referendum.
Despite this, a policeman was injured near a polling station in western Baghdad when a roadside bomb went off.
There have been other minor attacks by insurgents in Ramadi and near Basra.
Iraq's borders have been closed to non-essential traffic.
Private cars are banned from roads in many areas, and only a few people could be seen heading for the heavily-guarded schools-turned-polling stations.
Overnight, insurgents attacked power lines leading to the capital Baghdad, causing black-outs, but electricity was restored before dawn.
President Jalal Talabani and Prime Minister Ibrahim al-Jafaari were among the first to cast their ballots.
The president's and prime minister's vote inside the fortified Green Zone was shown live on Iraqi television.
"I voted Yes and I urge all Iraqis, no matter their different ethnicities and religions... to vote Yes to the constitution," Mr Talabani told reporters.
The BBC's James Reynolds in Baghdad says Kurds and the majority Shia Arabs are expected to approve the constitution, while Sunni Arabs - who make up a disaffected minority - are likely to either vote No or stay at home.
Sunni leaders fear the current proposals may lead the country to split, with a Kurdish north and Shia south, depriving Sunni Arabs of access to the country's oil resources.
In Washington, US Vice-President Dick Cheney said the US expected the constitution to be approved.
Public holiday
Some 15.5 million voters are expected to walk to the polling stations to register their view on the charter. Polls are set to close at 1800 (1500 GMT).
The election commission says it has managed to set up polling stations even in the regions worst-affected by violence, including the vast Anbar province, seen as the heartland of the insurgency.
Tens of thousands of troops and policemen have been drafted in to guard polling stations.
CONSTITUTION'S KEY POINTS
Iraq to be federal, parliamentary democracy
Official languages to be Arabic and Kurdish
Official religion to be Islam but religious freedoms guaranteed
Equal rights for all
Independent judiciary
Elections every four years
Q&A: Iraq referendum
A four-day public holiday is under way across the country, shutting government offices and schools. Baghdad airport has also been closed.
Private vehicles have been banned from the streets to prevent car bombers from targeting polling stations, and many voters will have to go on foot to cast their ballots.
Much of Baghdad was blacked-out for hours after dark as people broke the Ramadan fast.
"It was sabotage near Baiji," a town 180km (112 miles) of Baghdad, Electricity Ministry spokesman Mahmoud Saadi told the Reuters news agency.
Earlier, at least three polling stations in Baghdad came under fire from gunmen in passing cars, police said. No one was injured.
This constitution is a sham and will not prevent a civil war
John, Boise Idaho USA
Iraq constitution: Your views
Unidentified gunmen also attacked three offices of the largest Sunni Arab political party, the Iraqi Islamic Party, after it dropped its opposition to the draft text.
The BBC's Richard Galpin in Baghdad says the controversy surrounding the draft constitution has made campaigning much more adversarial than expected.
It has been easier for the Yes camp who dominate government to get their message across on state-controlled media than for the Sunni minority, our correspondent adds.
If voters in three of Iraq's 18 provinces muster a two-thirds majority against the constitution, it will fail.
The Sunnis are dominant in four provinces and so therefore effectively hold a power of veto if they turn out in large numbers to vote against it.
If the text passes, it will provide the basis for parliamentary elections.
The results of the referendum will not be declared for several days.