Europe's simmering crisis: Key EU challenges
EU leaders face a perfect storm of problems when they meet in Brussels on Thursday for another crisis summit.
Here we assess three of the toughest issues on the EU's agenda: migration, Brexit and jobs.
In his State of the Union speech last month, European Commission President Jean-Claude Juncker lamented the EU's current "existential crisis".
He warned that weak European "solidarity" was allowing the agenda to be set by anti-EU populists, scornful of liberal democracy.
To inspire young people, he said, the EU should launch a European Solidarity Corps by the end of this year. Young volunteers would be able to help in emergencies, including the refugee pressure points.
A stark illustration of Europe's lack of solidarity is an emergency scheme launched in 2015 to relocate 160,000 refugees.
The Visegrad Group (Poland, Hungary, the Czech Republic and Slovakia) opposes the policy, which applies only to Syrians and Eritreans with legitimate asylum claims.
As of 13 October, only 4,716 had been relocated from Greece - far below the target of 66,400. Out of a target of 39,600 to be relocated from Italy, only 1,316 had been moved. More than 144,000 migrants have arrived in Italy this year alone.
Resources in both countries are severely stretched, as most of the overcrowded migrant boats arrive there.
Italian Prime Minister Matteo Renzi said he would be "very tough" towards EU countries "shirking their commitments" in the migrant crisis. Their refusal to help ought to trigger cuts in EU funding, he said.
The EU has launched a common European Border and Coast Guard agency, with an initial deployment on Bulgaria's borders. It is part of efforts to prevent a repetition of last year's crisis, when more than a million irregular migrants arrived in the EU.
At least 1,500 border guards will be available for rapid deployment to pressure points such as the Greek islands. EU specialists are already working at "hotspots" in Greece and Italy - camps that register migrants and assess asylum claims.
The camps are controversial, not least because living conditions there are often squalid.
The migration challenge is complex and demands action on many fronts. The EU wants to speed up deportations of economic migrants, many of them from sub-Saharan Africa. But push factors fuelling the exodus are deep-rooted: conflicts and human rights abuses are rife in Africa and the Middle East.
Deciding on safe countries of origin is another thorny issue. The EU is sending many migrants back to Turkey now - a major transit country. Yet Turkey is hosting 2.7 million Syrian refugees, few of whom can get work.
The numbers reaching Greece from Turkey have fallen dramatically since the controversial Turkey deal took effect.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
The UK vote to pull out of the EU threatens to gouge a big hole in the EU budget. The UK's estimated net contribution was £8.5bn (€9.4bn; $10.4bn) in 2015, the House of Commons Library says.
On a per capita basis the UK made the third-largest net contribution to the budget in 2015. It was €215 per capita, behind the Netherlands (€331) and Sweden (€262).
Only Germany paid in more last year than the UK, though in previous years the French contribution had been similar to the UK's.
It remains to be seen which EU programmes, if any, the UK chooses to stay in after formal Brexit.
Businesses and many other stakeholders are worried about the uncertainty and lack of detail.
The EU refuses to hold even informal negotiations before Prime Minister Theresa May triggers the Article 50 exit clause. That should happen by next April.
EU officials say there will be no compromise over free movement of people - it is a condition for remaining in the EU single market.
European Council President Donald Tusk warned of a "hard Brexit", meaning the UK risks losing its single market advantages.
He mocked UK Foreign Secretary Boris Johnson's remark about the UK "having our cake and eating it" in a Brexit deal.
"Brexit will be a loss for all of us. There will be no cakes on the table," Mr Tusk said. "There will be only salt and vinegar."
Trade terms will be the big battleground - and the battle is likely to drag on for years.
That is why there is great attention now on the EU-Canada trade deal, Ceta, which could finally be launched early next year.
The Ceta negotiations began back in 2009, and still there is much unease about it in Europe. It might be a model for a Brexit deal - but the tensions also highlight the difficulties the UK faces.
The aftershocks of the 2008 financial crisis are still being felt in Europe. This month there was further bleak news from the banking sector: 20,000 jobs to be cut, including 9,600 at Germany's Commerzbank and 5,800 at Dutch bank ING.
The EU is slowly putting in place a Capital Markets Union, to diversify funding for businesses. The goal is to help businesses - especially start-ups - get venture capital or market funding. Despite the 2008 crash, banks dominate lending in Europe, yet debt problems have forced many to rein in business loans.
Unemployment remains stubbornly high. In June 2016 the highest jobless rates were in Greece (23.4%) and Spain (19.5%), Eurostat reports. Germany's rate in August was 4.2% - the lowest apart from the Czech Republic.
Nearly 21 million were unemployed EU-wide in August, 16.3m of them in the 19-nation eurozone.
Young hit hard
The picture is bleaker for young people, the under 25s. The youth unemployment rates in Greece and Spain in June 2016 were 47.7% and 45%, respectively. Italy's rate in August was also very high - 39%.
EU-wide, about 4.2m young people are unemployed, 3m of them in the eurozone.
The EU's Youth Guarantee scheme is targeted at the most precarious group - about 7.5m young people who are not in education, employment or training (Neets). It aims to ensure that within four months of leaving school or losing a job they get a good-quality job, further education or training.
The EU allocated €12.7bn to the scheme for 2014-2020, but the European Court of Auditors (ECA) says a funding shortfall from national governments has put the initiative at risk.
The UK is among several countries that chose not to participate. UK data for 2015 suggests that British support programmes for Neets reached only one in five of them.
The International Labour Organisation (ILO) said funding of about €21bn annually could make the scheme really effective.
The cost of having so many young people unemployed is enormous, in terms of benefit payments, lost earnings and taxes. The ECA estimates it to be €153bn annually.
In Spain, only one in 10 Neets has benefited from the Youth Guarantee, the daily El Pais reports. Spanish bureaucracy has been blamed.
The take-up is also poor in Italy, Hungary and Malta. In contrast, a majority of Neets in France and Germany have benefited from it.