Britain is poised to join the alliance after the Government gave the strongest indication yet that it would seek parliamentary approval for air strikes in Iraq as early as Saturday.
Talking to the Spectator, Defence Secretary Michael Fallon hinted British involvement could be extended to carrying out air strikes in Syria.
"Iraq is under attack not just from terrorists inside its own borders but it is under attack from terrorists in the north of Syria, and if Syria continues to be unwilling or unable to deal with [Isis] then at least the question arises as to whether we shouldn't assist Iraq in doing so," he said.
The Syrian Government was forewarned of the impending air strikes in a message sent by Samantha Power, the US Ambassador to the United Nations.
Washington has little option during a prolonged air campaign but to have some co-ordination with those fighting Isis on the ground: the Syrian Army, Hizbollah of Lebanon and the Syrian Kurds. Otherwise the US would have to avoid attacking Isis when the extremist group is battling any of these forces.
US Central Command says aircraft and Tomahawk cruise missiles from US naval vessels hit "fighters, training compounds, headquarters and command and control facilities, storage facilities, a finance centre, supply trucks and armed vehicles".
The strikes focused not only on the eastern third of Syria held by Isis but on its positions in Aleppo and Idlib.
Saudi Arabia, United Arab Emirates, Jordan, Qatar and Bahrain also assisted or took part in the strikes, their participation aimed at showing that the US is not launching an anti-Sunni crusade.
The Gulf monarchies' role is significant because in the past the US has identified private donors in these states as financing jihadis in Syria and Iraq.
The air strikes are unlikely to have inflicted critical damage on Isis, which has been expecting an air war.
People in Raqqa, the provincial city that has been Isis' Syrian headquarters, say militants had moved out of public buildings, hidden heavy weapons and told fighters' families to leave the city. "They are trying to keep on the move," one was quoted as saying. "They only meet in very limited gatherings."
The risk of air attacks will make it hard for Isis to continue to engage in semi-conventional warfare using columns of vehicles packed with heavily armed fighters to storm government-held positions in Syria and Iraq.
It will probably revert to guerrilla warfare, which has been its tactic in Iraq since the US started bombing there on August 8. In the past few days Isis fighters have killed 40 Iraqi soldiers with suicide bombs and captured a further 68 as well as over-running an army garrison west of Baghdad.
British Prime Minister David Cameron may announce today that Britain is ready to join air strikes in Iraq at the request of Baghdad, but not in Syria.
The ritual murders of two US journalists and a British aid worker have shifted public opinion in the US and Britain in favour of bombing Isis in Syria and Iraq, but not necessarily towards any wider part in the war.
The wars in Afghanistan and Iraq since 2003 have underlined the limitations of air power in achieving results against an elusive enemy.
As well as attacking Isis, the US struck at Jabhat al-Nusra, the Syrian representative of al-Qaeda which is focused in Idlib, northern Syria, and Deraa and Quneitra in the south.
The Syrian Observatory for Human Rights says at least 50 fighters and eight civilians were killed. Many may have belonged to an al-Qaeda-linked group, Khorasan, planning to target the US.
Jabhat al-Nusra was driven out of eastern Syria by Isis and has become weaker, though it appears to have been participating in a Western-backed offensive aimed at opening supply lines to rebel enclaves in Damascus.
The US is going to train and arm a "third force" of supposedly moderate Syrian rebels in a camp in Saudi Arabia, but past attempts to develop such a force have foundered.
Though air strikes will inflict casualties on Isis in Syria and Iraq, they will not be enough to defeat the group and may not even contain it. Much will depend on how far the US is prepared to give tactical support to those fighting Isis on the ground in Syria.
These are mostly groups of which the US Government disapproves or regards as terrorists, such as Hizbollah and the Syrian Kurds besieged by Isis at Kobani, also known as Ayn al-Arab, in northern Syria. The Kurdish militia defending the town belong to the YPG, which is part of the PKK Turkish party that the US has labelled terrorist.
In the past Isis has retaliated violently after any action against it so its opponents will be bracing themselves for a similar reaction.