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 capital at 0534 local time (0234 GMT), signalling the start of the US-led campaign to topple Iraqi leader 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.
Iraqi officials said some non-military targets had been hit and a number of civilians injured in Doura, a southern suburb of the capital.
Shortly before Baghdad air raid sirens sounded the all clear at 0600 GMT, Iraqi TV broadcast what it said was a live speech by Saddam Hussein.
"I don't need to remind you what you should do to defend our country," he said.
"Let the unbelievers go to hell... you will be victorious, Iraqi people."
Saddam Hussein is known to have several body doubles, but correspondents familiar with the Iraqi leader say they believe it to be him.
China has condemned the US attack, saying that the war was a violation of the UN charter and of international law.
BBC Defence Correspondent Jonathan Marcus says the attack was on a much smaller scale than had been expected for the opening of the conflict, and was probably mounted at short notice when US military planners spotted a good target.
The F-117s were probably already in the air, ready to attack if required, our correspondent says.
President Bush gave his order for the first strikes on Baghdad after being told by the CIA that it believed it knew the whereabouts of Saddam Hussein, the Washington Post reported.
CIA director George Tenet said he believed the Iraqi leader was meeting advisers in a suburban house in southern Baghdad, according to the newspaper.
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.
US officials said 2000-pound (900-kilogram) precision-guided bombs were dropped from F-117 Nighthawk stealth fighter-bombers.
More than 40 Tomahawk cruise missiles were also fired from six US Navy vessels, including two submarines, stationed in the Mediterranean, the Red Sea and the Persian Gulf, officials said.
The French AFP news agency 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, 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.
Two Iraqi missiles hit the northern Kuwait desert on Thursday, and there have also been reports of exchanges of artillery fire on the border.
Troops and reporters have been ordered to put on gas masks and protective suits.
The attack on Baghdad began after President Bush's 0100 GMT 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.
But UK Defence Minister Geoff Hoon said on Thursday that British forces were on "very, very high" state of alert and that it would not take long before the attack on Iraq escalated.