The UK left the EU at 23:00 GMT
Prime Minister Boris Johnson hailed the "dawn of a new era" in a video message
Brexiteers celebrated at a rally in a packed Parliament Square, London
Earlier, supporters of the EU held a procession through Whitehall to "bid a fond farewell" to the union
Labour leader Jeremy Corbyn urged the country not to "turn inwards" after it leaves the bloc
Scotland's First Minister Nicola Sturgeon says Brexit day is a "pivotal moment" for Scotland and the UK
EU chief Brexit negotiator Michel Barnier has been speaking to the BBC about the lessons to be learned from Brexit.
Michel Barnier: We are weaker than if we were together
Image source, PA MediaSir Keir Starmer says Labour needs to "make the case" for freedom of movement.
The leadership contender says that after Brexit he wants people to work, study and live in Europe as they can now.
Speaking in London, he adds: "We have to make the case for freedom of movement and we have to make it strongly."
He also says the UK should "welcome migrants" and not "scapegoat them", and that low wages and poor housing "are not the fault of migrants who've come here".
The vote to leave the EU, he says, was "a verdict on our failed economic and political system".
A Dutch fisherman tells the BBC why he is downbeat about Brexit.
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Image source, Getty ImagesTony Blair says Remainers must not look over their shoulders "in unrequited longing for what was".
The former Labour PM says he opposed Brexit "with every fibre of my political being" and still regrets the decision.
He also hits out at his party's "mind-boggling ineptitude", which he says "helped facilitate" Brexit happening.
But Mr Blair says the attitude of Remainers should now be "to strive to make the best of it [and] to approach it with determined optimism, not looking over our shoulders in unrequited longing for what was".
He adds: "No one in the country is going to thank us or think more of us if we behave churlishly in defeat and frankly the challenge of making Brexit work is sufficiently important for our nation, that we cannot afford to be absent from it.
"Britain is a great country. At our best, we are a great people. Our history shows us what our future can be. Time to embrace it."
A novel way of marking Brexit came to our attention today.
British Apples and Pears - guess who they represent? - were giving out leaflets, and yes, free apples, in Westminster with the exclamation: "A new dawn is breaking!"
In a leaflet, the organisation says it is renaming an apple Eos, after the Greek goddess of dawn, to "herald in the next chapter in our life outside the European Union".
The Union Jack carving was a particularly nice touch...
EU Commission chief tweets...
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Reality Check
The BBC Reality Check team has been trying to help with some of the practical things you need to know about what will change after Brexit.
These have been some of our most popular pieces on the subject:
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Victoria Derbyshire
Despite the protests of two people who back Remain, others on the Victoria Derbyshire programme are celebrating.
Brexit-backing Jake Gregory says it is "like the first day of the rest of our nation's life".
He adds: "I can't believe it is actually happened.
"We have managed to bat off all the Remainers and we are finally achieving it".
Image source, ReutersBusiness lobby group, the CBI, says the UK may be leaving the EU, but "our future prosperity remains connected".
The CBI's director general, Carolyn Fairbairn, says: “Despite the challenges of the last three years, together we have made progress.
"No deal has been avoided and a year of status quo gives time to shape that new relationship."
She adds: “Now the real work begins. It’s time to focus on the future and build a new relationship with Europe.
“This can reflect our shared values and mutual interest, and support bold global trade ambitions.”
Brexit supporters are in a party mood as they travel from Southampton to London for tonight's celebrations.
On the coach, the gang has champagne and song sheets as they serenade our reporter with Land of Hope and Glory.
The organiser of the trip, Julie Haylett, says: “It’s celebration not protest this time, let’s party!
"Who would have thought we would get there? They’ve thrown everything in our way.”
Brexit Day: Birmingham children try to explain it all
Schoolchildren at a Birmingham school have said they hope Brexit day doesn't lead to more arguments.
The Year Six pupils at Featherstone Primary School have been learning about democracy, Parliament and Brexit.
They gave their views on what the UK's exit from the EU might mean for the future.
Victoria Derbyshire
Mr Bray is joined in his disappointment by Ayo Adesina - who voted Leave but changed his mind.
He tells the BBC's Victoria Derbyshire programme he is "feeling completely devastated" as the UK leaves the EU.
"I think it is the wrong decision for the country," he adds.
"All the polling shows there is a consistent majority for us to remain in the EU now.
"Yes I voted to leave, but I have changed my mind since then.
"What we were told we were getting in 2016 is not what we are getting now."
The chancellor tweets from the train...
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Victoria Derbyshire
You may not know the name, but you will probably know of Steve Bray.
He's the man with the top hat and megaphone who has been shouting in Westminster (at volume) about the need for the UK to stay in the EU.
And on the day we leave, he hasn't changed his opinion.
Appearing on the BBC's Victoria Derbyshire programme, he says Brexit is "a disaster for us".
He adds: "Over half this nation do not want to be leaving the European Union.
"We were denied a second referendum or a confirmatory vote on what the actual deal would have been because they know that Remain would have been the answer."
Image source, PA MediaThe Irish Taoiseach says seeing the UK leave the EU today is "bittersweet".
But Leo Varadkar says he is looking forward to a "new alliance, a bespoke relationship between the European Union and the United Kingdom".
He adds: "When I met with Michel Barnier [the EU's chief Brexit negotiator] on Monday we were united in our belief that we will begin this new phase determined to secure the best outcome for the European Union and our future.
"We'll say goodbye to an old friend embarking on an adventure, their own tryst of destiny.
"We do hope it works out for them."
If not, "there will always be a seat for the United Kingdom, at the European table" he says.
Brexit Party MEP Widdecombe leaves leave EU Parliament, led by a bagpiper
Brexit Party MEPs have held a procession through Brussels, led by a bagpiper, as they celebrated their victory in leaving the EU.
Anne Widdecombe seemed to have little sympathy for those who regretted the decision to leave the EU.
She told reporters: "One side had to lose in that referendum.
"Would they have cared if we were sad? Would they have cared if we had lost? The answer is no.
"I would have been very sad if we had lost. But that is democracy, that is what it means. Somebody wins, somebody loses."
BBC Breakfast
Image source, EPACabinet minister and leading Brexit support Michael Gove says the UK wants to have "as close as possible a relationship with the EU" after we leave.
Speaking to BBC Breakfast, he reveals the government's plan is to build on the model the bloc has with Canada.
He says: “We want trade to be as frictionless as possible, but the EU is clear - you can only have fully frictionless trade if you accept all their rules, you accept all their laws, you're subordinate to their judges, you're subordinate to their political structures.
"But we voted to be independent."
Mr Gove adds: "We want to have as close as possible a relationship with the EU - and the approach we want to take is built on the relationship that they have with Canada.
"That means we want to have a relationship where there are ultimately no tariffs, no quotas on our trade, but there will be some regulations that will differ in Britain. We will do things in a way which is better for our economy."
He admits this may lead to some "bureaucratic processes there that aren't there now", but the minister adds: "We will do everything possible to minimise the friction in the interest of our country.”
A special cabinet meeting is taking place outside of London to mark the arrival of Brexit.
Ministers are heading to Sunderland via Kings Cross Station in London for the symbolic event.
Image source, PA MediaChancellor Sajid Javid arrives at Kings Cross with a smile
Image source, PA MediaHousing Secretary Robert Jenrick weaves his way through traffic on his way to the station
Image source, PA MediaBusiness Secretary Andrea Leadsom heads to the train
Image source, PA MediaBusiness Minister Kwasi Kwarteng looks happy as he joins his colleagues
Image source, ReutersThe First Minister of Scotland says tonight's departure from the EU will be "a moment of profound sadness for many of us across the UK".
In a speech in Edinburgh, Nicola Sturgeon - the leader of the SNP - says that moment will be "tinged with anger" as Scotland voted to remain in the EU.
But she says she wants to focus on "hope" going forward of "a different and better future for Scotland" - and this can only be achieved, she claims, through independence.
"Our task is to persuade a majority of people in Scotland to choose it," says Ms Sturgeon.
"We know that change is coming to Scotland. But it does not have to be the change the Tories want to impose upon us.
"A new independence referendum will put the decision about the best path for Scotland into our own hands.
"And there is a mandate from the public and from the Scottish Parliament for a referendum."