The UK, US and France have launched air strikes against Syrian targets after last week's alleged chemical weapons attack in Douma.
Overnight Royal Air Force Tornados bombarded a former missile site outside of Homs, while several sites around Damascus linked to Syria's chemical weapons programme were also targeted.
Donald Trump, Theresa May and Emmanuel Macron later held telephone conversations where they agreed the strikes had been "a success".
And this followed the US President declaring "Mission Accomplished!" in a tweet on Saturday afternoon.
"A perfectly executed strike last night. Thank you to France and the United Kingdom for their wisdom and the power of their fine Military. Could not have had a better result. Mission Accomplished!," he wrote.
The UK Government meanwhile has set out its legal basis for joining in the air strikes.
And the US has warned it is "locked and loaded" to strike again if chemical weapons are deployed in future by the Assad regime.
"This evil and despicable act left mothers and fathers and children thrashing in pain and gasping for air," he said.
"The combined American, British and French response will integrate all instruments of our national power."
Video report by ITV News Correspondent Juliet Bremner
But at a UN Security Council meeting on Saturday, Russia criticised the move.
Russia's ambassador to the UN said the strikes followed a "well tried" pattern of provocation, "mendacious" accusation, verdict and punishment.
The Kremlin said that Vladimir Putin in "the most serious way condemns the attack on Syria, where Russian servicemen are helping the legitimate government in its fight with terrorism".
In a speech outside of Downing Street, Mrs May said she hoped the air strikes served as a warning to Russia and Syria.
The Prime Minister insisted the military action was "legal" and defended the decision to go ahead without securing the backing of Parliament.
Mrs May said "every possible diplomatic channel" had been sought before the decision to launch targeted strikes had been taken.
"This persistent pattern of behaviour must be stopped - not just to protect innocent people in Syria from the horrific deaths and casualties caused by chemical weapons but also because we cannot allow the erosion of the international norm that prevents the use of these weapons," she said.
"This is not about intervening in a civil war. It is not about regime change.
"It is about a limited and targeted strike that does not further escalate tensions in the region and that does everything possible to prevent civilian casualties."
Later, the Government published a document setting out why it believed the military action was legal.
This included the UK being permitted under international law, in exceptional circumstances, to take measures to alleviate overwhelming human suffering.
In these circumstances, and as an exceptional measure on grounds of overwhelming humanitarian necessity, military intervention to strike carefully considered, specifically identified targets in order effectively to alleviate humanitarian distress by degrading the Syrian regime's chemical weapons capability and deterring further chemical weapons attacks was necessary and proportionate and therefore legally justifiable.
During the extraordinary UN Security Council meeting, called by Russia, the US warned against the future use of chemical weapons in Syria.
US ambassador Nikki Haley said the country was "locked and loaded", should a poisonous gas be used by the Assad regime.
"We are confident that we have crippled Syria's chemical weapons program. We are prepared to sustain this pressure, if the Syrian regime is foolish enough to test our will," she said.
"If the Syrian regime uses this poison gas again, the United States is locked and loaded."
NATO was quick to back the attack on Syria.
Secretary General Jens Stoltenberg said on Saturday that all 29 of its members supported the strike.
Labour leader Jeremy Corbyn said the military action against Syria was "legally questionable" and makes real accountability for war crimes less likely.
He said MPs should have been given a vote on the issue and called for "renewed diplomatic efforts" the bring the conflict in Syria to an end.
The air strikes were launched at 9pm EST (2am BST) and destroyed important infrastructure at three sites connected to the Syrian regime's chemical weapons programme.
General Joseph Dunford, chairman of the US Joint Chiefs of Staff, said the first was at a scientific research centre in greater Damascus, involved in the development and production of chemical warfare.
The second was at a chemical weapons storage facility west of Homs, while the third was at a chemical equipment storage facility and important command post.
He added: "Important infrastructure was destroyed which will result in a set-back for the Syrian regime. They will lose years of research and development, storage and equipment."
The MoD said the regime was "assessed to keep chemical weapon precursors stockpiled in breach of Syria's obligations under the Chemical Weapons Convention" at the site.
US Defence Secretary James Mattis and General Joe Dunford told reporters at a Pentagon briefing that the strikes were over and there had been no reports of any allied losses.
General Dunford described the operation as a "one time shot".
He said the only resistance was some Syrian surface-to-air missile activity.
General Dunford said there was no co-ordination with the Russians and "nor did we notify them".
Mr Mattis said double the number of weapons were used in the strikes compared with similar attacks on Syria carried out last year.
General Dunford said the strike had inflicted maximum damage without unnecessary risk to civilians.
Asked if the US and its allies would continue military operations, he said: "That will depend on Mr Assad should he decide to use more chemical weapons in the future, and of course the powers that have signed the Chemical Weapons Prohibition (Organisation for the Prohibition of Chemical Weapons) have every reason to challenge Assad should he choose to violate that.
"But right now this is a one-time shot and I believe that it sent a very strong message to dissuade him, to deter him from doing this again."
He added: "Right now we have no reports of losses."
Asked if there had been any Russian retaliation, General Dunford said: "We did have some initial surface-to-air missile activity from the Syrian regime. That's the only retaliatory action we're aware of at this time.
"We've completed the targets that were assigned to the United States central command. Those operations are complete."
He added: "We specifically identified these targets to mitigate the risk of Russian forces being involved. We did not do any co-ordination with the Russians on the strikes, nor did we pre-notify them."
The Russian military said Syria's Soviet-made air defence systems downed 71 out of 103 cruise missiles launched in the strike.
Colonel General Sergei Rudskoi of the Russian military's General Staff said the strike had not caused any casualties and Syrian military facilities targeted have suffered only minor damage.
He said the Russian air defence assets in Syria monitored the strike but did not engage any of the missiles.
In response to the strikes the Russian ambassador to the US, Anatoly Antonov, warned "that such actions will not be left without consequences".