- Europe's major centre-left and centre-right set to lose dozens of seats and their combined majority
- Green parties and some far-right parties saw surges
- Turnout across the EU rose to its highest for 20 years - 50.5% across all 28 member states
- In the UK, the Brexit Party is heading to a significant lead, amid losses for Conservatives and Labour
We are closing our international live coverage of the European elections for the night. You can continue to follow UK results and reaction here.
Here are the the day's main developments:
- The big power blocs of the centre-right and centre-left lost their combined majority in the European Parliament. "The monopoly of power is broken," said Denmark's Margrethe Vestager, the liberal candidate for the top post in the European Commission
- Europeans voted in their biggest numbers since 1994, bucking years of decline with a turnout just shy of 51%
- The big winners of the night were the liberals and Greens. The liberals have were boosted by the decision of President Macron's ruling party to join them
- The Greens saw strong votes in Finland, Germany, France and Portugal
- The nationalist right had a patchy night, but enjoyed successes in Italy, where figurehead Matteo Salvini ran to victory, and in France, where Marine Le Pen defeated the Renaissance alliance of Mr Macron.
- In the UK, the newly-formed Brexit Party soared to victory, gaining 28 seats amid massive losses for Conservatives and Labour
- There are still results to be announced, alliances to forge, and perhaps some domestic political fallout for parties across the continent
- BBC journalists will be covering the story from both UK and international angles - stay tuned for developments throughout the day
- To catch up, take a look at what we know so far about the outlook across Europe
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Hours ahead of a no-confidence vote which he could well lose, the Peoples Party (ÖVP) of Chancellor Sebastian Kurz has enjoyed a comfortable victory in the European elections. The Social Democrats have to decided to vote against his caretaker government, formed last week with a mix of technocrats and People's Party ministers. Mr Kurz's coalition with the far right collapsed in the aftermath of a video scandal surrounding two key far-right figures.
There was success for the ruling Law and Justice (PiS) party, with parliamentary elections on their way later this year. "We still have to win even more than now. This is a great challenge and we have to meet it," said party leader Jaroslaw Kaczynski.
It was an "unexpected comeback" for the Dutch Labour party, which won with 18% of the vote and double their seats. The Freedom party of Geert Wilders, the anti-Islam politician allied to the far right in Italy and France, may lose all four of their seats, although that is not confirmed.
A good night here for the ruling party of Prime Minister António Costa, who faces a general election in October.
Prime Minister Lars Lokke Rasmussen's Liberal Party won in Denmark, taking five seats after a record voter turnout of 66%. The other big story of the night was the Eurosceptic Danish People's Party(DF) losing around two-thirds of their votes. Danish voters return to the polls on 5 June for parliamentary elections.
It hasn't been a big success across the board for right-wing nationalists in Europe, but their flag-bearer, Matteo Salvini, is enjoying a big victory in Italy. His League party has polled over 30%, well ahead of the centre-left Democratic Party (PD). Mr Salvini's populist coalition partners, Five Star, are behind the PD in third. When Italy voted in general elections last year it was Five Star who won.
"We are Italy's first party, now for change in Europe," declared Mr Salvini, whose ambition is to build a big, nationalist bloc.
A big success here for the conservative New Democracy party, which has gained four seats. Not only that, the centre-right victory has prompted left-wing Syriza's prime minister, Alexis Tsipras, to announce snap elections a few months early.
The European Parliament is currently putting turnout across the entire European Union at 50.95% - a 20-year high.
Numbers have not been that high since 1994, when the EU was much smaller (and 56.67% of voters turned out).
The highest turnout was in Belgium (89%) where voting is compulsory, as it is in Luxembourg (84%).
For big increases in turnout look to Spain (64.3%), Austria (59%), Germany (61.5%) and Denmark (66%).
The low-turnout countries include Slovakia, which actually saw an increase from 13% to 22.7%. The Czech Republic, Slovenia and Croatia were also below 30%. In the UK, turnout was an estimated 37%, up from 35.6% in 2014.
It's been a difficult night for centre-left parties in much of Europe.
Labour and Socialist parties have topped the polls in Portugal and the Netherlands. And in Spain, Socialist Prime Minister Pedro Sánchez is enjoying his second election victory in a month.
His PSOE party may even be the biggest component of the Socialists and Democrats group in the Parliament – with a projected 20 seats out of the group's projected 152 – and 32.8% of the vote. That's higher than the 29% they polled on 29 April.
The centre-right Popular Party came second while far-right Vox, which broke through last month with more than 10% of the vote, has seen a reverse, with a projected 6.2% of the vote.
If you want an indicator of how difficult this election has been for Britain's two largest parties, look to the leadership.
Prime Minister Theresa May's Conservative Party came third in her own constituency - losing to the Brexit Party and Liberal Democrats.
And her opposite number, Jeremy Corbyn of the Labour Party, saw his party come second to to the Liberal Democrats - and it was his birthday on Sunday, too.Copyright: EPA
BBC Europe editor Katya Adler tweets:
There's a reason why they're labelled provisional – the data from the European Parliament for the Czech Republic has been revised. Compared to the first version, the Social Democrats have "lost" their only predicted seat. They had four in the previous parliament so they could face total wipeout.
The parties in the ALDE and Left groups have also been docked one each.
The winners out of the revised (but still provisional) results are the Conservatives and the Centre Right. Prime Minister Andrej Babis's ANO is on course to gain two seats.
Slovakia elected a liberal president in Zuzana Caputova in March, bucking Europe's overall movement away from the centre. Now a coalition of two liberal parties have won the European Parliament election too, with 20% of the vote, the BBC's Rob Cameron reports.
That pushes the ruling leftist SMER into second. Turnout is always woeful in Slovakia - but it has gone up from 13% in 2014 to 22.7%.
And take at look at Portugal too. No far-right party came anywhere near winning a seat and the ruling Socialists appear to have gained votes, with exit polls giving them over 30% of the vote.
And unlike most countries in the EU, turnout in Portugal went down from 34% to 30%, our Lisbon correspondent Alison Roberts tells us.
The ruling Fidesz party of Prime Minister Viktor Orban is on course for a big win. Fidesz has been suspended from the centre-right EPP in the European Parliament and Mr Orban's projected 13 seats could go elsewhere. But this shows how dominant his party still is.
We reported the results from Finland earlier, but here is how those seats are allocated: