The US launched a major attack on Islamic State (IS) militants in Syria this week.

MPs are being recalled to parliament later to vote on whether Britain should join in with military action against the jihadist group.

Is the case for intervention stronger this time than it was in 2003, when Tony Blair took Britain to war against Saddam Hussein in a move later condemned as illegal by the secretary general of the United Nations?

What are the Americans doing?

The US launched a wave of airstrikes against IS on Tuesday, using fighters, bombers and Tomahawk missiles.

The Pentagon said the attacks had been a success but cautioned that it could take years to defeat the Sunni Islamist group completely.

IS has declared an Islamic caliphate in territory that stretches across Syria and neighbouring Iraq. The group is responsible for a string of atrocities including attacks on minority groups and the murders of foreign journalists and aid workers.

The Syrian Observatory for Human Rights, a monitoring group opposed to the regime of Bashar al-Assad, says air strikes have so far killed at least 13 civilians, including five children.

The Americans stress that they are not acting alone, having enlisted the support dozens of countries.

The US state department lists more than 50 other countries who have made “contributions and commitments”.

More than a dozen, including Britain “have contributed to the military effort, either by providing arms, equipment, training, or advising” local enemies of IS, principally Kurdish peshmerga fighters.

Arab countries who back the US-led campaign include Bahrain, Saudi Arabia, Jordan and the United Arab Emirates.

France has already joined in air strikes in Iraq, and now Britain looks likely to follow suit if, as expected, the prime minister wins a Commons vote tomorrow.

What does David Cameron want?

Mr Cameron says he wants Britain to join air strikes against IS targets in Iraq. He has ruled out putting British boots on the ground.

It has been widely reported that British special forces are in fact operating in Iraq but the government never officially comments on such stories.

Mr Cameron has said he wants to limit the terms of today’s vote to action in Iraq. He has not ruled out hitting IS targets in Syria, but that will require another Commons vote.

Labour leader Ed Miliband says Labour will vote with the government to approve air strikes in Iraq. Syria is more complicated: Mr Miliband says he supports the US attacks on IS targets there too, but he wants a UN Security Council resolution.

Why do we need a vote?

There is actually no constitutional requirement for governments to seek parliamentary approval before committing UK forces overseas – a prime minister can send troops into action using royal prerogative powers.

But it has been a convention for military action to be rubber-stamped by the House of Commons since Tony Blair put the invasion of Iraq to a vote in 2003.

Of course, the legal case for the war against Saddam has been very widely criticised for the lack of UN approval and the weakness of the evidence that the dictator was amassing an arsenal of weapons of mass destruction.

What is the legal case for intervening in Iraq now?

We’ve spoken to a number of international law experts and there is a broad consensus that attacking IS targets in Iraq should not present Mr Cameron with any legal difficulties.

This is because the Iraqi government has specifically asked international allies for aerial support to help it fight IS.

Governments have the right to defend themselves from armed attack and can ask other countries for help, so action in Iraq would fall under the principle of collective self-defence as set out in article 51 of the UN charter.

Professor Craig Barker from the University of Sussex told us: “If there is evidence of a clear request to go in, I can’t see there being a major legal issue.”

What about Syria?

Here’s where the law gets more complicated and the experts start to disagree.

The basic problem is that the Assad regime has not asked for air strikes. A UN security council resolution could approve military action, but pro-Assad Russia is likely to wield its veto and block such a move.

Some commentators, including the former attorney general Dominic Grieve and the US ambassador to the UN Samantha Power, have suggested that air strikes on Syria could still be considered legal without a resolution, but there are a range of opinions on this.

Professor Marc Weller from Cambridge University agrees with the US position that strikes on Syria are “still lawful, provided the action is focused on supporting the operation in Iraq”.

This is because the threat to Iraq comes from a neighbour that has arguably proved incapable of dealing with militants using it as a base. If Syria is harbouring terrorists and cannot deal with them, Iraq’s right to defend itself could extend to cross-border action.

Prof Weller said: “That is covered by the request Iraq has made to support it in relation to its own security. You can invoke the right of self-defence since Syria is unable or unwilling to to remove the source of the threat.”

Professor Dapo Akande from Oxford University agreed, saying self-defence had similarly been used to justify the US invasion of Afghanistan and, more controversially, Israeli incursions into Lebanon to attack Hamas militants.

Mr Grieve said a more recent body of international law dealing with military intervention for humanitarian reasons provides the justification for strikes against targets in Syria.

Professor Iain Scobbie from London’s School of Oriental and African Studies told us he thinks both arguments are weak, saying there is no “clear mandate for the use of force” in countries that harbour militants, and the idea of humanitarian concerns providing a moral case for war “really doesn’t have traction” in international law.

Other legal experts have expressed similar doubts about the US case for action in Syria.

Whatever the legal rights and wrongs, there is no mechanism for the US actually being prosecuted for breaching international law. Rulings at the International Court of Justice are only binding on countries that accept its jurisdiction.

The court of world public opinion is the one that really counts, according to Professor Barker.

“Part of international law is rhetoric. It’s about the Americans in particular cloaking themselves in some sort of dialogue of international law.”