Of the around 27,000 foreign fighters believed to have travelled to Syria and Iraq to take up arms alongside extremist groups such as the Islamic State, around 5,000-6,000 are estimated to be European.
But with some slipping in and out of Europe unnoticed, the exact figure is unknown.
The EU's anti-terrorism coordinator, Gilles de Kerchove, believes that between 2,000 and 2,500 European nationals or residents are still in the Middle East but are likely to return as anti-IS fighters close in on the jihadists' last strongholds such as Raqqa in Syria.
"The most recent figures suggest that 15 percent to 20 percent of European fighters have died there, 30-35 percent have already come back and around 50 percent are still in Syria and Iraq," De Kerchove wrote in a recent report.
Those who have not returned home are holed up "in pockets of resistance in neighbouring countries or will travel to other conflict zones", he added.
'Desire to attack'
The EU's security commissioner Julian King said in March that the jihadist threat "will remain high in the coming months and years, particularly as events in Syria, Iraq and Libya unfold".
Some of the foreign fighters will attempt to return to EU countries, "some with the intention of planning and executing potential future attacks", he said.
Although attacks this year in Stockholm, Manchester and London were carried out by "homegrown" extremists who had not fought in Iraq and Syria, security services fear battle-hardened extremists pose a high risk.
According to a count by AFP's European bureaus, based on official estimates, around 1,500 jihadists have already returned to their home countries or countries of residence.
They are often either put in prison, or placed under surveillance, sometimes with stringent conditions and sometimes in de-radicalisation programmes whose success remains unproven for the time being.
French journalist and author David Thomson, who has written a best-selling book about returning jihadists called "Les Revenants", said the biggest challenge for the authorities was evaluating what exactly they did in Iraq and Syria.
"The problem is when they're questioned after they return, they all say they were nurses," he told AFP.
Slip through net
The biggest problem for investigators is finding proof of what the individual did, Thomson said.
"The most cunning, and often the most dangerous, never post anything about their activities on social networks.
"So in France as a rule it leads to prison, and with longer and longer prison sentences. The problem is just pushed back because no-one knows what else to do for the time being."
When returnees set foot back in EU countries, they are first arrested, then questioned and put under investigation.
Different countries have each come up with specific charges to correspond to the problem of returning jihadists, such as "membership of a terrorist organisation".
A breakdown done by AFP showed there are currently 280 suspected jihadists who have returned to Germany out of 820 who went to Iraq and Syria, 450 in Britain out of 850, 210 in France out of around 1,000 and 45 in the Netherlands out of at least 280.
In Norway the figure is around 40 from 100 who went, in Sweden it is 150 (out of 300), in Finland 20 (out of 80) and in Denmark around 70 (out of 145).
In Austria, of the 300 people who went to fight at least half are of Chechen origin. Around 40 were killed and 50 were arrested on their return.
Karl-Heinz Grunboeck, an Austrian foreign ministry spokesman, said there were two consequences for the returning jihadists.
"The first is that they are charged with membership of a terrorist organisation. We investigate to see if they have a criminal past. Then they are placed under police surveillance to assess the risks that they might pose," he said.
"If they have dual nationality they could be stripped of their Austrian nationality, but that only concerns a very small number of cases."
In the absence of a common EU policy, many governments are playing it tough, but some countries have tried to engage in dialogue with the returnees -- with varying degrees of success.
The Danish city of Aarhus, for example, began a rehabilitation programme in 2007 focusing on helping former radicals find a job or with training and accommodation.
Phil Gurski, a researcher at the International Centre for Counter-Terrorism in The Hague, said countries were "struggling" with what to do with returnees.
"Some will come back traumatised, some will be wounded, some may want to disown IS and its barbarity and (other returnees) may be keen to radicalise others," he told AFP.
"Governments will have to consider a variety of strategies to deal with the phenomenon that is unprecedented on such a scale in recent history."