Donald Trump acknowledges "many, many" Cubans were killed during what he calls the "brilliant" military operation in which Venezuela's President Nicolás Maduro was seized
Local media reports 23 Venezuelan and 32 Cuban soldiers died when US elite troops stormed Maduro's compound - the BBC's Will Grant examines the close security ties between Venezuela and Cuba
In Caracas, armed police are seen patrolling the streets, in an image shared by Interior Minister Diosdado Cabello
And in a video shared online, the security forces are filmed shouting "loyal always, traitors never"
Meanwhile, our correspondent Jonathan Beale reports the US is tracking a tanker nearing Europe that it tried to board last month in the Caribbean
We're still hearing plenty of reaction to the US's dramatic action in Venezuela over the weekend.
Over on BBC Radio 5 Live, Nicky Campbell is hosting a phone-in asking the question, Venezuela: was Trump right?
To follow along, watch the programme live at the top of the page.
Davide Ghiglione
Reporting from Rome
Image source, ReutersItalian Prime Minister Giorgia Meloni says she spoke by phone with Venezuelan opposition leader Maria Corina Machado on Sunday.
Both agreed that the exit of President Nicolas Maduro would create prospects for a peaceful and democratic transition.
“During the phone call, it was agreed that Maduro’s exit opens a new chapter of hope for the people of Venezuela, who will be able to once again enjoy the basic principles of democracy and the rule of law,” Meloni’s office said in a statement.
Image source, Getty ImagesWilkie was the secretary for military veterans and under secretary of defence for readiness in Trump's first administration
A member of the first Trump administration says he has not seen "any plans as to how we expect to manage the next few days".
Robert Wilkie, who served as under secretary of defence for readiness, tells BBC Radio 4's Today programme the operation to seize Maduro was "flawless" in military terms, but his concern in such missions is "What is the next day?"
He cites Vietnam, Iraq and Afghanistan as examples of "American overreach".
"Once you launch that, what happens next? We don't have a very good track record when it comes to those things."
But he also says he believes US authorities have discussed plans for a stabilisation force in Venezuela with its military.
Wilkie stresses the operation was "certainly" legal under American law "because [Maduro] is an illegitimate leader".
"The indictment… gives the president incredible leeway to conduct operations, to remove a criminal and international threat to the people of the US."
"Being a Venezuelan at the moment is very hard and strange," one Venezuelan living in the UK tells BBC Radio 5 Live.
Sofia (not her real name) says she feels "happy, excited, scared, emotional and angry" since Maduro was seized - but feels like people in the country can't "freely voice our feelings about what has happened."
She frequently returns to the country on business or to visit family and says the people in Venezuela are "very quiet" because they are scared.
For Sofia, she doesn't want America to rule over her country, but she thinks the US took a "corrupt person in a country that has no democracy."
Tom Bennett
Live reporter
Image source, Getty ImagesFlores, right, has been in a relationship with Maduro since the 1990s. The pair married in 2013
When US forces conducted a night raid on the Venezuelan capital Caracas, they didn't just drag President Nicolás Maduro from his compound and put him on a flight to New York - they took his wife too.
Cilia Flores, 69, has long been seen as one of the most powerful figures in Venezuela, a political operator in her own right who for decades has shaped the country's fortunes.
After years leading Venezuela's National Assembly, she helped consolidate her husband's grip on power after his 2013 presidential election victory.
As First Lady, she was dubbed "First Warrior" by Maduro. But in that role she publicly took a backseat - presenting a more family-oriented face to what critics say was a brutal regime.
She hosted a TV show, Con Cilia en Familia, and made occasional appearances on state television to dance salsa with her husband. But behind-the-scenes, she is thought to have been one of Maduro's key advisers, and an architect of his political survival.
Flores has faced allegations of corruption and nepotism, and in recent years her family members have been found guilty in US courts of cocaine smuggling.
She will now face drug trafficking and weapons charges in a New York court, along with her husband.
Will Grant
Latin America correspondent
Cuba has confirmed 32 of its citizens were killed during the US operation to seize Nicolás Maduro.
The communist-run country - which relies on Venezuelan oil - had supplied much of Maduro’s security detail and has personnel throughout the Venezuelan military.
Two days of national mourning have been declared with Cuba’s President Miguel Diaz-Canel saying he honoured "the brave Cuban combatants who fell taking on the terrorists in imperial uniforms who kidnapped and illegally removed the Venezuelan president and his wife from their country."
Asked about wider military action, Donald Trump said it wouldn't be needed against Cuba as it was likely to fall on its own.
But he didn't rule out intervention in Colombia, describing its left-wing president Gustavo Petro as a drug trafficker and a "sick man".
Petro has denied the accusations, warning Trump not to slander him.
US spies had been monitoring Venezuelan President Nicolás Maduro’s every move for months - observing where he slept, what he ate, and what he wore - before the mission to seize him was finalised in early December.
It became a two-hour-and-twenty-minute mission by air, land and sea stunned many in Washington and around the world on Saturday. Here’s how it unfolded:
For full details, read our breakdown here.
Venezuela has been left with "the leftovers of the Maduro regime," a former political prisoner tells the BBC.
Freddy Guevara, who was an opposition politician in the country, tells BBC Radio 4's Today programme he felt the US would ensure a "democratic transition."
He says there are many "critiques" of the US, but "it’s a country with democratic institutions and a long tradition of freedom, and I quite frankly can’t imagine a United States government supporting a dictatorship in Latin America".
He adds that Maduro's regime had only been sustained "by force and fear" and relied upon international support.
Image source, ReutersDelcy Rodríguez is due to be sworn in later as Venezuela's president, hours after Donald Trump warned her she could pay a "very big price" if she "doesn't do what's right".
In comments to the Atlantic on Sunday, the US president said: "If she doesn't do what's right, she is going to pay a very big price, probably bigger than Maduro."
He added that for Venezuela: "Regime change, anything you want to call it, is better than what you have right now. Can't get any worse".
Trump has vowed the US will run the country until "a safe and proper and judicious transition" is possible. He also promised US oil companies will move into the country to fix infrastructure "and start making money for the country".
We'll bring you live images of Rodríguez's swearing in as and when we receive them.
Nicolás Maduro has been charged with "Narco-Terrorism Conspiracy, Cocaine Importation Conspiracy, Possession of Machineguns and Destructive Devices, and Conspiracy to Possess Machineguns and Destructive Devices against the United States".
President Trump has described the charges brought against Maduro as responding to his "campaign of deadly narco-terrorism" against the US and its citizens.
But this notion is built on "very flimsy ground," says Julia Buxton, professor of justice studies at Liverpool John Moores University.
She tells BBC Breakfast that Venezuela is "not a major exporter of cocaine".
"The bulk of cocaine going into the US comes through the Pacific Coast, up through Mexico and Colombia.
"There's no fentanyl coming out of Venezuela. What the trump administration has had to do is kind of invent this notion of Maduro as a narco-terrorist in order to carry out policies of regime change."
She says that Trump would like to see American oil companies move into Venezuela, but this isn’t a particularly attractive prospect for those companies.
"There's a glut of oil on global markets, and to try and turn around Venezuela's oil industry is going to take billions and billions of dollars in investment," she adds.
Tom Bateman
US State Department correspondent
Nicolas Maduro is being held in the Metropolitan Detention Center in Brooklyn, a notoriously overcrowded and unsanitary facility known for a history of violent incidents.
From there, he will be taken to federal court along with his wife Cilia Flores to be told of the charges they face - a 25-page indictment details allegations the couple enriched themselves from a violent crime ring smuggling tons of cocaine to the US.
Maduro has long rejected that as simply a pretext to force him from power.
The couple will enter their pleas with any bail request unlikely to be granted. President Trump has doubled down on his assertion that the US will now run Venezuela; demanding what he called total access to its oil industry.
There is no attempt by the White House to downplay the sense of coercion, with the US president again warning of a further military attack if Maduro's remaining allies in power fail to do his bidding.
When asked to comment on their claim Maduro had been kidnapped by the US, Trump said that wasn’t a bad term.
In the last 24 hours, Americans have appeared to support Trump’s actions in Venezuela, US political consultant and commentator Frank Luntz tells the BBC.
Luntz says that the American public does not "like, accept or tolerate drugs coming into the country."
"It's more than just drug running and shipping... it's an issue of the role that Cuba's playing, China, Russia, and even Iran are playing," he tells BBC Breakfast.
However, he emphasises that the Americans do not "want boots on the ground" in Venezuela.
"So, there's going to be a wait and see among the American population," he adds.
Image source, ReutersDelcy Rodríguez - now Venezuela's acting president - is a loyal lieutenant of Maduro, often appearing at events side-by-side with the president and his wife.
A lawyer and diplomat, she has held various political offices under Maduro.
As his vice-president, Rodriguez, 56, was part of his inner circle - describing him as the "only president" while demanding his release.
On Saturday, Donald Trump said US Secretary of State Marco Rubio had been talking to Rodríguez, who had expressed her willingness to do "whatever the US asks".
This was at odds with Rodríguez publicly refusing that Venezuela would become "a colony of an empire".
But at her first cabinet meeting on Sunday she struck a more conciliatory tone, calling for the US to collaborate with Venezuela.
Image source, Delctrodriguezv/InstagramVenezuela's acting president says her country is commited to peace and prioritises moving towards "balanced and respectful" relations with the US.
In a statement Delcy Rodriguez invites the US government to "collaborate with us on an agenda of cooperation" within the framework of international law.
"President Donald Trump, our peoples and our region deserve peace and dialogue, not war," she says before concluding: "Venezuela has the right to peace, development, sovereignty and a future."
Jeremy Bowen
International editor
Image source, EPAThe Maduro operation amounts to another serious blow to the idea that the best way to run the world is to follow an agreed set of rules, as laid out in international law.
The idea was tattered before Donald Trump took office, but he has already demonstrated repeatedly both in the US and internationally that he believes he can ignore laws he doesn't like.
A few hours before Maduro and his wife were seized, he met Chinese diplomats at his palace in Caracas.
China condemned the US action. It said "hegemonic acts of the US seriously violate international law and Venezuela's sovereignty and threaten peace and security in Latin America and the Caribbean region".
The US should "stop violating other countries' sovereignty and security".
Even so, China might see a precedent set by the US action.
It regards Taiwan as a breakaway province and has declared that returning it to control of Beijing is a national priority.
Donald Trump seems to believe that he makes the rules, and what applies to the US under his command does not mean others can expect the same privileges.
But that is not how the world of power works.
Image source, HANDOUTMaduro (R) pictured with his wife Cilia Flores
On Sunday, US Attorney General Pam Bondi outlined the charges brought against the Venezuelan President and his wife Cilia Flores.
Nicolás Maduro has been charged with "Narco-Terrorism Conspiracy, Cocaine Importation Conspiracy, Possession of Machineguns and Destructive Devices, and Conspiracy to Possess Machineguns and Destructive Devices against the United States".
Later, President Trump summed these charges up as Maduro's "campaign of deadly narco-terrorism" against the US and its citizens.
Maduro has previously denied being the leader of a drug cartel.
Trump also called Maduro an "illegitimate dictator", adding that he had asked the Venezuelan leader to "surrender" a week before the strikes.
Bondi says that Maduro and his wife will "face the full wrath of American justice on American soil in American courts".
The pair are now in custody at a New York detention centre. Their court appearance could take place later today.
Maia Davies
Live reporter
It’s just over 48 hours since the US military stormed Nicolás Maduro's home in the early hours of Saturday, seizing the Venezuelan president and his wife.
The pair have since been flown to the US and could appear in a New York court as early as today on various drugs and weapons charges.
President Trump says the US will run Venezuela and take care of the country’s oil infrastructure, while Secretary of State Marco Rubio says the action doesn't mean the US is at war with the country.
Venezuela's new interim president - Maduro’s Vice President Delcy Rodriguez - has invited the US government to “collaborate” with them and says its people "deserve peace and dialogue, not war."
The situation follows months of increasing pressure from Washington on Venezuela, with Trump accusing Maduro of drug-trafficking and narco-terrorism - accusations he denies.
Stay with us as we bring you the latest throughout the day.