Who will replace European Commission President Jean-Claude Juncker?
It is all change at the heart of the EU, and the key role of Commission president is up for grabs as Jean-Claude Juncker prepares to pass the baton at the end of October. But who will take his place?
May elections have left the European Parliament more fragmented and the chances of reaching consensus more difficult.
Heavyweights France and Germany have already clashed over the role, which includes proposing new European laws and providing political guidance.
So who is in the running, based on what we know so far? There are official candidates - and some who are not yet candidates at all.
Manfred Weber, European People's Party
For: A high-flyer in the EU's influential centre-right bloc, he is the closest this contest has to a front-runner.
The 46-year-old Bavarian, whose candidacy has been endorsed by prominent leaders such as German Chancellor Angela Merkel and Austrian Chancellor Sebastian Kurz, has served as leader of the European People's Party (EPP) since 2014.
Against: The EPP may be the biggest grouping in Parliament but it has lost ground in the elections and Mr Weber will have to secure the support of other groups if he is to win.
French President Emmanuel Macron has shown no indication of his support for Mr Weber, and with environmental issues coming to the fore and a surge in Green MEPs elected in May, it will not help that his centre-right colleagues have been accused of voting against climate change measures.
What he says: He spoke recently about the importance of strengthening security across the bloc and the need to protect the "European way of life". In a Twitter post in November, which featured a promotional video, he wrote: "Here and everywhere else people are asking us to bring Europe back home."
He has promised to appoint a commissioner to oversee a new relationship with Africa to help control migration to Europe, and has said that future trade deals with other countries should include clauses banning child labour.
Margrethe Vestager, Liberals
For: A big name in Danish politics, Ms Vestager has spent the past five years as competition commissioner, spearheading EU anti-trust investigations that have ended in big fines for technology giants Google and Apple.
Her battle to protect consumers and make large firms pay earned her the wrath of US President Donald Trump last year, who is reported to have told Mr Juncker following news of the hefty fines: "Your tax lady, she really hates the US."
Against: Ms Vestager is certainly causing a buzz and the Liberal ALDE group gained ground in the elections, partly thanks to the arrival of President Macron's party. But the Liberals have fielded a slate of seven candidates for the EU job, and one Commission colleague says her choice is out of the question as she was not even a lead candidate.
What she says: "I have worked with breaking monopolies. This is also what voters have been doing. The monopoly of power is broken," she declared after the elections that broke the majority of the two big centre-right and centre-left blocs in the European Parliament.
Frans Timmermans, Party of European Socialists
For: Frans Timmermans has the wind in his sails, having led the Dutch centre-left Labour party to a dramatic, unexpected victory in the European elections, winning 19% of the vote on the back of a pro-European campaign.
Mr Timmermans is First Vice-President of the European Commission, helping to steer through EU legislation banning plastic straws and negotiating the EU's deal with Turkey to reduce the flow of migrants.
He was lampooned in the run-up to the May vote by political opponents as Eurocrat "Hans Brusselmans"; but the negative message failed and the multi-lingual Labour leader took advantage of his election campaign to push for the Commission presidency.
Against: He is widely disliked in Poland and Hungary for challenging their governments over rule of law.
What he says: Warning of the risks of nationalism he said last month: "People who used to vote for my party and many parties here are now voting for nationalist parties, sometimes even extremist parties. That's our fault," he said. He also spoken of Brexit as leaving the UK looking like "Game of Thrones on steroids".
His latest policy proposals for the bloc include a minimum rate of corporation tax across the EU of 18%, and the implementation of a minimum wage in every member state.
Ska Keller of the Greens
For: After the Green surge in the May elections, her grouping is now the fourth biggest in Parliament and environmental issues have become key to the EU's agenda over the next five years. In her home country, Germany, the Greens are currently leading in the opinion polls.
Ska Keller has already stood once as Green "Spitzenkandidat" (top candidate) in 2014, and is as focused on the rights of migrants as she is addressing the plight of the environment. She has previously demanded that future EU agreements contain better protections for human rights.
She became a MEP in 2009 at the age of 27 and has said that, while she aims to represent everybody, young people in particular need a louder voice in Europe.
She has a master's in Islamic Studies, Turkology and Jewish Studies and is social media savvy, posting regularly on Twitter to her more than 45,000 followers.
Against: Up against the other candidates, Ms Keller is likely to struggle to find the support of enough member states. And as it is the member states who have the job of nominating a candidate for approval by the Parliament, they are more likely to go for one of the bigger names.
What she says: Ska Keller wants to tackle climate change but not through banning air travel. "If trains become cheaper and better, we'll make short-haul flights redundant."
Kristalina Georgieva, World Bank chief executive
For: The Bulgarian economist is not even a candidate so she is a long shot, but as a high-flying East European she definitely has a chance.
Ms Georgieva, 65, is highly regarded among European leaders for overseeing a reduction in the bloc's spending while serving as EU budget commissioner between 2014 and 2016. During that time she was also vice-president of the Commission.
She has managed one of the world's largest humanitarian aid budgets, garnering a reputation while doing so as an outspoken champion of gender equality.
She has worked alongside Bill Gates and former UN Secretary General Ban Ki-moon to raise the issue of climate change to the forefront of the bloc's policy agenda.
With all that and her background in the centre-right EPP, she could act as a unifying candidate for member states opposed to Manfred Weber.
Against: She is not yet a candidate and Parliament may object to someone who has not been part of the race. Parliament says the winner has to be one "who made his/her programme and personality known prior to the elections, and engaged in a European-wide campaign".
What she says: "My grandparents had very little education. My parents finished high school. I was the first in my extended family to get a PhD. From a village in Bulgaria to CEO of the @worldbank -- this is what possibility looks like," she writes on her Twitter page.
Michel Barnier, EU chief Brexit negotiator
For: He may not be a candidate, but few EU figures have had a profile as dominant as this 68-year-old former French foreign minister who succeeded in keeping 27 countries on the same page during the bloc's Brexit negotiations with the UK.
He is admired by President Macron who said last month that he was "one of the European leaders that have eminent qualities and can be on the list [of candidates for EU top jobs]".
Against: Once said by former French President Nicolas Sarkozy to possess the "charisma of an oyster", Mr Barnier is known for choosing his words carefully and has a precise manner when addressing leaders - often with a formidable stare.
He is also known for backing the legacy of post-war President Charles de Gaulle, who advocated a centralised economy, powerful presidency and independent foreign policy.
The secretary-general of European journalists, Fabrice Pozzoli-Montenay, told the BBC that Mr Barnier had in recent years seen Gaullism as the defence and protection of the European Union.
What he says: "Now more than ever, we Europeans need collective action in defence of our values and a rules-based international order. This could be Europe's moment, based on a more robust and decisive European Union." (January 2019 opinion piece)
Angela Merkel, Germany's Chancellor
For: Still sitting at the top of the list of most powerful women in the world, according to Forbes, the woman once dubbed the Empress of Europe is relinquishing her role as German chancellor in 2021 - a decision that sparked widespread speculation over what will happen next.
Mrs Merkel was said by Mr Juncker himself to be "highly qualified" for a senior EU role, telling Germany's Funke media group in April that she was "not only a person of respect, but also a complete and endearing work of art".
Against: The 64-year-old is the Brussels rumour mill's favourite fantasy candidate, despite previously saying that she would not seek a role in a political office after stepping down in 2021, and appearing to show no interest in the job whatsoever.
Although her coalition with the centre-left Social Democrats is in jeopardy and she is no longer party leader, she is not really in a position to take up the presidency anyway.
What she says: "I as a member of the EPP family will of course work to support Manfred Weber."
Dates in the race
June: Consultations between EU leaders and parliamentary groups
20-21 June: European Council meets to decide a candidate by qualified majority vote
July: European Parliament votes on nominee for Commission president by a simple majority
1 November: New Commission president takes office