Even if they have no battleground experience, those who decide to undertake solo attacks, like the two recently in New York, in the name of the Islamic State group or Al-Qaeda are almost impossible to detect in advance.
"In France, the US, or elsewhere, there certainly won't be any more large attacks planned from abroad like those of November 13, 2015 in Paris," said Marc Sageman, a former CIA agent and terror expert, referring to the multi-pronged IS operation that left 130 dead.
"Ever since then, attackers here or in Europe have not been guided by IS but acted on their own, imagining themselves to be soldiers of an imagined Islamic community which they want to defend or avenge."
Neither Akayed Ullah, the Bangladeshi immigrant who tried to blow up a New York subway station last week, mainly wounding himself, nor Sayfullo Saipov, an Uzbek who mowed down people on a New York bike path on October 31, killing 8, had any evident contact with Islamic State jihadists aside from watching their propaganda videos.
Experts say that kind of self-radicalised attacker, completely unknown to authorities, is the main threat countries face today.
Safe haven in a bedroom
While returning IS fighters are definitely a threat, "it's not a primary concern," said Albert Ford of the New America think tank.
"The attacks in this country were made by people who were in the country for years. The real danger is with these not very sophisticated but deadly attacks that we saw lately in New York."
According to New America data, 85 percent of the 415 people accused of Islamist-related crimes in the United States since the September 11, 2001 attacks have been American citizens. Of them, 207 were born in the United States.
They also were not known to law enforcement: only one fourth had a police record.
"None of the deadly jihadist attacks in the United States since 2014 had a known operational connection to ISIS or its networks," a New America report says, using another acronym for the Islamic State group.
On both sides of the Atlantic, homegrown attacks "are obviously the most dangerous," echoed Thomas Sanderson of the Center for Strategic and International Studies' Transnational Threats Project.
"Of the 19 last major attacks in Europe, 17 did not have a direct foreign factor element to it."
Homegrown attackers stay under the radar, giving little away that would alert police, Sanderson noted.
"Their safe haven is their bedrooms. They can prepare at home, they don't need the footprint of a camp anywhere," he said.
Overseas threat from IS remains
At the same time, experts say, the threat from IS in Syria and Iraq has not disappeared even if the group has been expelled from nearly all of the territory it held.
For those who survive, according to former US undersecretary of defense for intelligence Michael Vickers,the war isn't over.
"Defeating insurgencies always takes time. It ranges from ten years to multi decades. And this one is a global insurgency, with expanded space and expanded time," he said.
Indeed, the Islamic State group planned for battlefield losses and has a strategy for surviving, noted Bruce Hoffman, a Georgetown University national security expert.
"Two or three years before the Paris attacks, ISIS put in place an external operations network. This network extends beyond Europe," he noted.
"The traction of that strategy was demonstrated last May when a bomb attack was committed in Manchester, England, against a concert venue. That attack was operated by an ISIS cell operating out of Benghazi, Libya."
And the returnees, even if they stand a much higher chance of being spotted by police than self-radicalized homegrown attackers, are still part of that network, added Sanderson.
Even if returnees' numbers have been low, he said, "the returning fighters present a massive potential problem because of the skills and the credibility and the motivation."