WASHINGTON — The brothers who carried out suicide bombings in Brussels last week had long, violent criminal records and had been regarded internationally as potential terrorists. But in San Bernardino, Calif., last year, one of the attackers was a county health inspector who lived a life of apparent suburban normality.

And then there are the dozens of other young American men and women who have been arrested over the past year for trying to help the Islamic State. Their backgrounds are so diverse that they defy a single profile.

What turns people toward violence — and whether they can be steered away from it — are questions that have bedeviled governments around the world for generations. Those questions have taken on fresh urgency with the rise of the Islamic State and the string of attacks in Europe and the United States. Despite millions of dollars of government-sponsored research, and a much-publicized White House pledge to find answers, there is still nothing close to a consensus on why someone becomes a terrorist.

“After all this funding and this flurry of publications, with each new terrorist incident we realize that we are no closer to answering our original question about what leads people to turn to political violence,” Marc Sageman, a psychologist and a longtime government consultant, wrote in the journal Terrorism and Political Violence in 2014. “The same worn-out questions are raised over and over again, and we still have no compelling answers.”