US President George W Bush has launched war on Baghdad, vowing to "disarm Iraq and to free its people".
The strikes began at dawn
Mr Bush delivered a live television address shortly after explosions rocked the Iraqi capital, signalling the start of the US-led campaign to topple Saddam Hussein.
US military sources have told the BBC that five key members of the Iraqi regime, including Saddam Hussein, were targeted in the first attacks.
It is not known whether the targets were hit and what damage might have been caused.
The BBC defence correspondent says the attack was on a much smaller scale than had been expected for the opening of the conflict, and it had probably been mounted at short notice.
Speaking from the Oval Office, President Bush said American and coalition forces were in the "early stages of military operations" and had struck "targets of military importance".
He promised a "broad and concerted campaign" and said the US would prevail.
But, he warned, the campaign could be "longer and more difficult than some predict".
As dawn broke in Baghdad, anti-aircraft artillery peppered the sky as deep, heavy thuds were heard in the outskirts of the city.
The same target, in the east, is reported to have been hit three or four times.
Republic of Iraq Radio in Baghdad said that "the evil ones, the enemies of God, the homeland and humanity, have committed the stupidity of aggression against our homeland and people".
Reports quoting American military officials said planes had struck "targets of opportunity" which were thought to be occupied by elements of the Iraqi leadership.
US officials said Tomahawk cruise missiles were fired from F-117 Nighthawk stealth fighter-bombers.
French news agency AFP quoted a Pentagon official as saying the first strikes were "a limited thing - it ain't A-Day," referring to the planned massive air campaign.
A BBC correspondent in Baghdad said anti-aircraft guns were in action for about 15 minutes, after which the city became quiet again.
After the first strike, at 0534 local time (0234 GMT), a large pall of black smoke was seen in the south of Baghdad.
At about the same time as the strikes began, the US military appeared to take over a frequency of Iraqi radio with an Arabic-speaking presenter announcing: "This is the day we have been waiting for."
Our correspondent in Baghdad says the timing of the attack is unusual - coming as it did in daylight.
He says traffic remains normal and people are beginning to appear on the streets.
The attack began after President Bush's 0100GMT deadline for Saddam Hussein to go into exile or face war expired.
As the deadline approached, US-led combat troops in the Gulf - numbering about 150,000 - took up battle positions for an imminent invasion of Iraq.
A British military spokesman in Kuwait says no order has yet been given to the US and British troops who are waiting on the Iraqi border.
As forces moved towards Iraq on Wednesday, 17 Iraqi soldiers surrendered to American troops on the Kuwaiti border.
With battle looming the UN Secretary General Kofi Annan said his thoughts were with the ordinary people of Iraq as they faced the "disaster of war".
He warned the US and UK that "under international law, the responsibility for protecting civilians in conflict falls on the belligerents".
The Turkish Government, meanwhile, has asked parliament to allow US planes to use its air space, and it is expected to vote on the issue on Thursday.