Here is what we know so far about the strikes:
The strikes were aimed at "chemical weapons infrastructure" in what the US billed as a warning against Assad employing such weapons in the future -- a warning he has been accused of flouting in the past.
Over 100 missiles fired at Syria, 'significant number' intercepted: Moscow
They targeted a scientific research facility in the Damascus area, a chemical weapons storage facility west of the city of Homs and a third location that contained both a command post and a chemical weapons equipment storage facility in the same area, the US military said.
US General Joe Dunford, chairman of the Joint Chiefs of Staff, said there were no plans for further operations and indicated they took pains to avoid hitting any military assets of Russia, which supports Assad's regime.
An AFP correspondent in Damascus heard a series of huge blasts at 4:00am local time. For around 45 minutes, explosions echoed and the sound of warplanes roared over the city. As dawn broke, plumes of smoke could be seen rising from the city's north and east.
British jets struck "a former missile base... where the regime is assessed to keep chemical weapon precursors," the country's defence ministry said.
The Syrian Observatory for Human Rights monitoring group said that the "scientific research centers" and "several military bases" hit in the strikes had been "completely evacuated".
Russia says Syria chemical attack 'staged' with help of foreign secret service
Syrian state news agency SANA reported several missiles hit a research centre in Barzeh, north of Damascus, "destroying a building that included scientific labs and a training centre".
France announced that the combined strikes had destroyed a "large part" of Damascus's stocks of chemical weapons.
US, British and French "naval and air assets" took part in the strikes, which US defense chief James Mattis said employed more than twice the amount of munitions used during American strikes in Syria last year, in which 59 Tomahawk missiles were fired.
Britain's defense ministry said that four Tornado jets had fired Storm Shadow missiles at the base west of Homs. France said it fired three cruise missiles from frigates in the Mediterranean and nine from Rafale fighter jets deployed from home bases. The US reportedly used B-1 bombers in the strikes, but the American military declined to provide specifics.
The Russian military said the allies had fired a total of 103 cruise missiles, but that Syrian air defense systems managed to intercept 71 of them.
Syria fired surface-to-air missiles in response to the attacks but Russia apparently did not, the US said, despite a threat from the country's ambassador to Lebanon that Moscow's forces would do so.
Syrian state media reported only three people injured, while Russia's defence ministry said there were "no victims" among Syrian civilians and military personnel.
Syrian state news termed the strikes "a flagrant violation of international law" and said the intervention "is doomed to fail."
Russia's foreign ministry said the strikes came as Syria -- which has been wracked by seven years of civil war -- had "a chance of a peaceful future," while Moscow's ambassador to Washington warned of unspecified "consequences".
Syria's war: major regime victories
The Kremlin also severely condemned what it called an "act of aggression" and called an emergency session of the United Nations Security Council.
Opposition US Democratic lawmakers warned that any broader military campaign would require authorisation from Congress, as well as a well-formulated strategic vision.
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