Military experts have their say on what happens next
Lord Dannatt, former head of the British Army, writing in the Mail on Sunday, said it was "wholly right" that Syria was subject to sanctions from the UK, US and France following the "appalling" use of alleged chemical weapons by the Assad regime.
The Chief of the General Staff from 2006 to 2009, wrote:
"The Prime Minister...deserves our congratulations for having the moral courage to do the right thing at the right time.
"Always seeking approval from Parliament is a recipe for inaction."
Inaction, he says, would have made the West look weak.
He added that the next step for the UK is to play its part in getting all parties to meet "around the conference table" in Geneva, to put a stop to the Syrian civil war.
Lord West, former head of the Royal Navy, writing in a column for the Sunday Mirror, said that some form of military action "had to be taken" over the situation in Syria.
He wrote that Saturday's attack was a "pinprick" and the next one could be a "great big hammer".
The former First Sea Lord and Chief of the Naval Staff from 2002 to 2006, said Assad would be "stupid" to consider using chemical weapons again, although he said the attack on Douma was a fabrication.
Agreeing with Lord Dannatt, Lord West said in the column that "Theresa May was right not to go to Parliament".
He added that he believes Russia will not fire missiles, as he said "that would be an act of war". He believes President Putin will be happy to "allow this to fade away".
Professor Michael Clarke, a counter-terrorism and defence expert, warns the result of British involvement in strikes on Syria could be "cyber warfare".
Speaking to the Sunday Mirror, he said that an attack could be imminent in the next few weeks.
"I suspect Russia will choose not to respond in military terms. But cyber warfare is highly likely.
"It will be an attack on national infrastructure, not just upsetting city firms, but getting inside the transport system, or the health system, or air traffic control. It could affect everyone."
The response from politicians
Theresa May’s decision to launch strikes on Syria alongside the US and France were met with both support and criticism by politicians across the UK.
The Prime Minister’s decision came despite demands from opposition parties that Parliament was consulted before any military action was taken.
Foreign Secretary Boris Johnson wrote on Twitter that the world was:
"United in its disgust for any use of chemical weapons, but especially against civilians"
Labour leader Jeremy Corbyn said he would be pushing for the Government to release the legal advice it has received on action and demanding it goes back to the United Nations to get a new resolution.
He told broadcasters the use of chemical weapons was "appalling and disgusting".
The Labour leader added: "The consequences of any country taking unilateral action that has no legal basis are that it's an encouragement for others to do exactly the same and reduces our ability to complain when others do that."
Mr Corbyn said the role of Britain was to be an "honest broker" in trying to bring Russia and the US together in agreement at the UN.
He said Russia and the US had reached an agreement in 2013 on Syria.
"There is precedent that this process can work, and surely it would have been better to do that than start bombing - and goodness knows what the consequences of the bombing could be."
Support was voiced by other Tory MPs, with Thornbury and Yate MP Luke Hall saying: "Speed is essential. A clear signal to anyone who believes they can use chemical weapons with impunity."
Newark MP Robert Jenrick said:
"My thoughts are with our servicemen and women - and those of our US and French allies.”
“The cost to President Assad of using heinous chemical weapons must be higher than any perceived benefit. I strongly support the PM's decision."
However, the Scottish National Party spokesman for defence, Stewart McDonald, described the action as a "gesture bombing with no major international consensus".
"Most worrying is that she has acted at the behest of presidential tweets and sidelined Parliament," he said on Twitter.
"What does this new bombing campaign do to help move Syria towards peace? Nothing.
"Instead, it has the potential to dangerously complicate the war, making matters on the ground worse for the people that the strikes are supposed to help. There is no peace strategy."
Labour MP Owen Smith attacked the decision, writing on Twitter: "The House of Commons is elected to represent the people of our country and to hold our Executive to account.
"Parliament should have been recalled and consulted before we engaged in this military action in Syria."
European Council president Donald Tusk said the European Union would stand with its allies "on the side of justice".
"Strikes by US, France and UK make it clear that Syrian regime together with Russia & Iran cannot continue this human tragedy, at least not without cost," he wrote on Twitter.
Scottish First Minister Nicola Sturgeon also said questions remained about how peace could be brought to Syria.
She wrote: "My first thoughts this morning are with the service personnel called to action.
"Syria's use of chemical weapons is sickening - but the question that the PM has not answered is how this action, taken without parliamentary approval, will halt their use or bring long-term peace."
Welsh First Minister Carwyn Jones offered support to the Prime Minister before the attack took place. In a statement, he wrote: "I offered my support to any intervention that could prevent a further atrocity, but it is vital that any action forms part of a wider long-term plan for the region."
"Our thoughts today are with our service personnel and the people of Syria who have endured beyond all measure."