Latest results indicate a decline in support for centre-right and centre-left parties in the European elections, with some of the votes going to green, liberal and far-right parties instead.
Turnout was higher than expected, with some observers suggesting this was due to more young people voting.
In 2014 the centre-right and centre-left had more than half the seats in the European Parliament – but this is set to change.
Full results are expected overnight.
1. Centre falls away
In Germany Chancellor Angela Merkel’s centre-right Christian Democrats got 28% of the vote – their worst-ever performance in European elections. Meanwhile the centre-left Social Democrats (SPD) also did poorly, coming third with 16%.
In the European Parliament in Strasbourg, they provide MEPs to the centre-right European People’s Party (EPP) and centre-left Socialists and Democrats (S&D) respectively.
The EPP and S&D have always held more than half of the seats between them.
But official projections based on exit polls now say the EPP and S&D could lose about 92 seats, bringing their share of down to 42.6% – a drop of more than 12%.
However another centrist grouping, the Alliance of Liberals and Democrats for Europe (ALDE), is set to increase its share to 102 seats from 67 in 2014. French President Emmanuel Macron’s La République En Marche is set to join the group and it could play a kingmaker role.
Outgoing ALDE group leader Guy Verhofstadt hailed a “historical moment” because of what he said was a “new balance of power”.
2. Green wave
Many European countries have seen a rise in the Green vote, from the Nordic countries to Portugal.
In Germany the Green party more than doubled its vote share to come second with 22%.
The BBC’s Jenny Hill in Berlin says the Green party captured the zeitgeist while the other parties have struggled to put together a coherent environmental policy.
Our correspondent says about a third of those under the age of 30 voted Green. In the run-up to the vote 90 influential YouTubers urged followers to vote for parties that took climate issues seriously. They told voters to avoid the AfD, which they said denied climate change was even happening.
In France, green group Europe Écologie Les Verts (EELV) is on course to come third with 13.2%. Both Mrs Le Pen and Mr Macron have emphasised their green credentials. Mr Macron wants to shift to green technology and energy while Mrs Le Pen said her brand of localism was good for the environment.
In Portugal, the green PAN party (People-Animals-Nature) is on course to win its first ever seat in the European Parliament, possibly even two.
The Greens have won a historic second place in Finland but in Sweden, home to climate activist Greta Thunberg, they have gone into reverse. They are projected to poll 9.5%, down almost 6%.
In Ireland, early exit polls give the Green party 15%.
3. Mixed picture for nationalist right
In France Marine Le Pen’s National Rally party – formerly the National Front – is heading for first place with 23.4% of the vote, narrowly ahead of President Emmanuel Macron’s centrist grouping, which got 22.4%.
Turnout was reportedly high in areas where her party has previously done well and also in areas where support for the anti-government “gilets jaunes” (yellow-vest) movement is strong. Mrs Le Pen has changed her position on EU membership, saying she now wants to stay in the bloc.
In Germany the far-right AfD is predicted to get under 11%, up from 7.1% in 2014. In the Netherlands the Forum for Democracy and the Freedom Party of Dutch anti-Islam politician Geert Wilders together won nearly 16%, but Mr Wilders’ party has seen a steep decline.
Results in Spain give new far-right Vox party getting only 6.2% of the vote, down from the 10.3% it achieved in Spain’s national election.
In the UK a new anti-EU party, the Brexit Party is heading for victory at the expense of the Conservative Party, while pro-EU Liberal Democrats are taking votes from the traditionally centre-left Labour party.
Far-right and Eurosceptic parties are currently split between three groupings in the European Parliament – the European Conservatives and Reformists (ECR) and the two far-right groupings Europe of Freedom and Direct Democracy (EFDD) and Europe of Nations and Freedom (ENF).
However, Matteo Salvini, whose right-wing nationalist League party is predicted to win the Italian vote, is hoping to found a new grouping, the European Alliance for People and Nations, with the support of several parties.
What happened where?
The ruling People’s Party (ÖVP) has won with a record 34.9%, despite a scandal that has led to the collapse of its coalition government with the far right. ÖVP leader Sebastian Kurz is facing a no-confidence vote on Monday which could put him out of a job.
The far-right Freedom Party (FPÖ) – which quit the government after its leader Heinz-Christian Strache was exposed in a video sting – does not appear to have been that badly affected by the scandal. It came in third place with 17.5% of the vote, down only slightly from 2014.
Far-right Flemish party Vlaams Belang got 4.3% in the European election – but won a much larger 14% of the vote in the country’s federal election, held at the same time.
Initial results give the governing HDZ four of the 12 available seats. The centre-left SDP party gets 18.5%, seen as a disappointing result.
The Finnish Green party (VIHR) won 15.9% of the vote, coming behind the centre-right KOK party with 20.7% but ahead of the centre-left SDP with 14.7%.
It’s been a bad night for Prime Minister Alexis Tsipras’s left-wing Syriza party which has been beaten by opposition conservative New Democracy party. First official projections give New Democracy a nine-point lead.
Mr Tsipras has said he will call snap elections, which may take place at the end of June.
New Democracy leader Kyriakos Mitsotakis has called on Mr Tsipras to resign.
The centre-right Fine Gael party of Prime Minister Leo Varadkar is heading for a big victory, exit polls suggest. But Ireland’s electoral system means the results will take some time to come through.
The Dutch Labour party has won, as expected, with 18% of the vote. It’s a dramatic victory for Labour, who have been celebrating “an unexpected comeback”.
Green party PAN is set to enter the European Parliament. No pollster or projection had predicted this.