By John Simpson
World affairs editor, BBC News, Baghdad
The extraordinary, turbulent, hugely controversial life of Saddam Hussein was brought to an end at dawn this morning, between 0530 and 0545 local time, just as the call to prayer was sounding across Baghdad.
Saddam carried a copy of the Koran to his execution
A small group of Iraqis, including a representative of the Iraqi prime minister and a Sunni Muslim cleric, were brought to witness the execution.
It took place in an Iraqi compound known by the Americans as 'Camp Justice', a secure facility in the northern Baghdad suburb of Khadimeya, outside the Green Zone.
Several recent executions have taken place here.
Barzan al-Tikriti, Saddam's half brother, and the former chief judge Alwad al-Bandar, who were sentenced to death alongside Saddam, were not with him. They will be executed at a later date.
Saddam was brought in carrying a copy of the Koran, and the sentence was read out to him.
He was quiet, but handed the Koran to one of the people there and asked that it should be given to a friend, whom he named.
One of the four executioners told Saddam that he had ruined the country; Saddam responded firmly but quietly.
The noose was placed around his neck. He repeated the Muslim statement of faith.
When the chief executioner went to put the hood over his head, Saddam made it clear he wanted to die without it. It was his last action of defiance.
Then the trap door was released and he was hanged. The entire business took just a few minutes.
There had been concerns that people might not believe that Saddam was really dead, so the execution was videoed.
This is the end of an important and terrible chapter in Iraq's history. How Iraqis respond to it depends on their politics and their religious and ethnic background.
The Shia and Kurdish majority here will largely be overjoyed, and the government, which is itself mostly Shia, sees the execution as an important way of winning popular support.
To the Sunni minority, already embittered and in despair at losing political power, this is the final evidence that they are the major losers in the events of the past few years.
Like virtually everything in Saddam's long political life, reaching back to the early 1960s, his overthrow, trial and execution have divided opinion fiercely, both here and around the world.
His unusual name - Saddam - means "the one who confronts", and that is what he has done for almost half a century, invading first Iran and then Kuwait.
His first trial for mass murder, beginning in 2005, was supposed to be the Nuremberg Trial of our time. Yet, as ever, it proved to be divisive, and certainly did not receive general international approval.
There were questions about the nature of the evidence, and the Iraqi government intervened to sack the leading judge for not being tough enough in dealing with Saddam.
After he was sentenced to death, the appeals for clemency from many international leaders have been ignored.
These things will certainly continue to affect the way the world will see Saddam's death.
But now he has finally been swept off the political chessboard, the Iraqi government hopes that 2007 will be a better year as a result.