The terrorist slaughter and siege in a Nairobi shopping mall may be just a taste of things to come in the United States. The headlines from overseas over the last couple of days—a suicide attack on a Christian church in Pakistan; horrific bombings in Iraq—can seem like background noise in distant lands. But they should be reminders that the threat many Americans thought was behind them continues with a vengeance. Osama bin Laden is dead, yes, but the al Qaeda ideology that preaches hatred for nonbelievers and a special loathing for the United States lives on. It has spread like a disease, and the infection—terror—is still out there.

As if taunting the West, a Twitter feed identified with Al-Shabab offered up names and nationalities of seven of the alleged gunmen. All the names appear to be Somali—but the hometowns include Minneapolis, St. Paul, and Kansas City, Missouri, in the United States; London; and Helsinki.

One example of the global impact could be seen almost immediately on the streets of New York as news broke of events in Nairobi. Squads of patrol cars on heightened alert swarmed around possible terror targets in Manhattan, and the so-called Hercules teams of the NYPD, trained and outfitted for urban combat in the case of a terrorist attack, were deployed as well. “There is no specific threat to the city,” said John McCarthy, the NYPD spokesman, but “we keep track of events as they unfold across the globe, and we adjust our counterterrorism program accordingly.”

The fact that the core al Qaeda organization and its many affiliates are under huge pressure from American drone attacks, U.S. special-forces operations, and multinational military offensives is not exactly a consolation. There is a long record showing that when these groups are cornered on their home turf, they try harder than ever to take revenge on their enemies abroad. Their regional designs fail and their global ambitions increase. Many analysts thought bin Laden was on the ropes in early 2001. He and his acolytes and allies had tried to build revolutionary movements in Algeria and Egypt, and they’d suffered utter defeat. The September 11 attacks were plotted, not least, to prove they could still be effective.

“The real story is the resilience of these organizations that are supposed to be dead or down on their knees,” says one senior American intelligence officer, a veteran of the shadow wars against al Qaeda who is still in the trenches and prefers to remain anonymous. Those groups that are granted formal recognition by al Qaeda—among them Al-Shabab—are vowing their commitment to the long war.

Heightening the risk is the fact that al Qaeda affiliates under pressure today no longer feel compelled to carry out such massive, complicated operations as 9/11. They know they can command the world’s attention with much smaller attacks. Even when those fail, like the attempt to blow up an America airliner over Detroit with an “underpants bomb” on Christmas Day 2010, they create consternation and controversy. Increasingly these groups hit soft targets: places where people think they are perfectly safe and where they let down their guard.

That is precisely the case in Nairobi, where at least 59 people have been killed at Westgate Shopping Mall in the ongoing siege. It's favorite gathering place for the Kenyan elite and foreigners living in Nairobi. Among the dead are relatives of Kenyan President Uhuru Kenyatta, the wife of a U.S. diplomat working for the U.S. Agency for International Development, two French citizens, two Canadians, and a Chinese woman.

Many in Kenya, and in the Kenyan government, knew that attacks might be coming. After the Kenyan military moved into Somalia to help crush the Al-Shabaab organization there, threats of revenge proliferated and reverberated. Since the bloody siege in Mumbai, India, which was waged by another Al-Qaeda affiliate in 2008, Western officials have worried the tactic of armed gunmen attacking public buildings, killing bystanders, taking hostages, and fighting to the last man, would spread.

The Al-Shabab link is of particular concern in the United States. The group has attracted scores of young Americans to its ranks over the years, most but not all of them of Somali origin. One nightmare scenario for counterterror officials would be for some of them to return to the United States with their guerrilla and terrorist skills.

In Minnesota, the Mall of America reportedly holds lockdown drills for employees twice a month. These are mainly a precaution against random violence, like the shootings in Washington last week. But even before Kenya, everyone in the counterterror business was aware that the Mall of America could be a terrorist target, and it’s not irrelevant that many young men from the large Somali-American community in Minneapolis have joined Al-Shabab in the past.

How, exactly, do you guard against people willing to slaughter innocents as they work, or shop or play, far from any battlefield or confrontation?

That is a question still being debated in the United States, where the means used to gather intelligence about terrorist activities—which went almost unquestioned after 9/11—have now become the focus of angry public scrutiny. The National Security Agency’s massive data mining of telephone and Internet communications, revealed in detail by whistleblower Edward Snowden, has caused great public concern about privacy. The New York City Police Department’s efforts to track potential terrorists in Muslim communities have tarnished what was a sterling reputation, putting even the popular NYPD commissioner, Ray Kelly, on the defensive.

“The threat of terrorism is as great, if not greater, than it was before the World Trade Center was destroyed,” Kelly warned in a speech earlier this month. “From al Qaeda’s perspective, the war it waged on the streets of lower Manhattan on 9/11 continues in theaters from the U.S. to Europe to Indonesia to West Africa.” Kelly listed several plots over the last te10n months “with a nexus to New York City,” including the plan by the Boston Marathon bombers to carry out further attacks in Manhattan. Yet, as Kelly noted, not a single candidate running for mayor of New York this month asked for a briefing from the police or offered a picture of a plan to protect the city. It was as if they thought the threat had gone away.

In fact, we should all be giving the question of how to address this menace some new and serious thought. The Bush administration’s Global War on Terror may be over, but the terrorists’ global war on us is not.