All eyes are on Brussels to see who will win the race to succeed Jean-Claude Juncker as the head of the EU’s executive body on 1 November.
The EU’s inbox will be full to overflowing when Juncker leaves office on 31 October.
Top of the pile will be relations with Britain, which is set to leave the 28-nation bloc on or before that date.
The favourite to win the Conservative Party leadership contest, Boris Johnson, has said the UK must leave by 31 October and has said he would leave with no deal if he was unable to negotiate a better deal than Theresa May produced.
But also on the new EU president's desk will be the issue of what to do about the enlargement of the bloc into the Balkans.
Next week EU leaders will discuss Albania and North Macedonia's applications to join the bloc. When he took up his post in 2014 Juncker said no countries would join during his term, and it will be up to his successor to decide whether to speed up the entry of Tirana and Skopje.
EU foreign policy chief Federica Mogherini warned last month that Europe was "at a crossroads" when it comes to enlargement in the Balkans.
She said: "Failure to recognise and respond to objective progress would damage the European Union's credibility."
So who is in the frame and how are they likely to view the future of the EU?
Manfred Weber
The favourite is probably Manfred Weber, who has the backing of the influential conservative European People's Party (EPP), which includes members of Germany’s ruling Christian Democrats.
The 46-year-old Bavarian, whose candidacy has been endorsed by German Chancellor Angela Merkel and Austrian Chancellor Sebastian Kurz, has been the EPP’s leader in Brussels since 2014.
He has promised to appoint a commissioner to oversee a new relationship with Africa in a bid to control migration to Europe and also vowed to insert special clauses in trade deals with the developing world which would specifically ban child labour.
Weber is also a strong proponent of the idea of a European Union army.
He said: "It's a fundamental idea to never have war again in Europe. It’s today unthinkable, and with a common European army it would be totally unthinkable."
The EPP is far less influential than before last month's elections - it has 179 seats, compared with 216 in 2014.
French President Emmanuel Macron said on Tuesday, 11 June, he would support Mrs Merkel herself if she wanted the job.
Mr Macron said the EU "needs someone strong" at the helm and he said: "If she were to want it, I would support her."
But Mrs Merkel said last month she does not want the job and has thrown her weight behind Mr Weber.
Mrs Merkel said in October she would not seek re-election after her fourth term as Chancellor ends in 2021.
Frans Timmermans
Also strongly fancied for the job is Dutchman Frans Timmermans, who has the backing of the centre-left Party of European Socialists (PES).
Timmermans, who is First Vice-President of the European Commission, led his own Dutch Labour Party to victory in the European elections and played a vital part in steering through EU laws which banned plastic straws.
His political opponents in the Netherlands call him "Hans Brusselmans" and accuse him of being a creature of the eurocrats and, like Donald Tusk, he is loathed by the Polish and Hungarian governments, after he challenged legislative changes they made which he claimed were illegal under EU law.
Timmermans has a way of throwing out juicy quotes for the media - last month he said Brexit was like "Game of Thrones on steroids."
If he replaced Juncker, Timmermans would try to force each EU member to set corporation tax at no lower than 18 percent - it is currently just nine percent in Hungary - and make them introduce a minimum wage.
Ska Keller
The Greens had a strong European election last month and increased their number of MEPs from 52 to 75, although seven of those were in Britain and would obviously go with Brexit.
Ska Keller, a 37-year-old German, is the only female candidate and offers a much more radical agenda than the other contenders.
She is putting climate change much higher up her agenda than migration and says: "The poor will be hit hardest by climate change."
Keller is violently opposed - or as violent as a pacifist could be - to the proposed formation of a European Army.
Guy Verhofstadt
While the EPP and PES have both backed a single candidate the Alliance of Liberals and Democrats for Europe (ALDE) group has eschewed that process and has instead announced support for seven possible candidates.
They include Belgium’s Guy Verhofstadt, an outspoken critic of Theresa May and the Brexiteers.
Another liberal contender is Margrethe Vestager, from Denmark, who has spent the past five years as competition commissioner and has led the EU anti-trust investigations into Google and Apple.
Michel Barnier
There are several other names floating around in the ether, even though they are not official candidates for the post.
Among them is Michel Barnier, who is much admired in Brussels for the tough line he took with David Davis and Dominic Raab while negotiating the Brexit deal.
Kristalina Georgieva
Another possible runner, and a complete outsider, is the Bulgarian economist who is chief economist at the World Bank.
Ms Georgieva, 65, was EU budget commissioner between 2014 and 2016 and managed to rein in spending.
Her support would come from the EPP and she might be more palatable to those who are not naturally disposed to Mr Weber.
But she needs to declare herself as a candidate soon because the European Parliament has already stated the President has to be someone who "made his/her programme and personality known prior to the elections, and engaged in a European-wide campaign."