And the problem of extremists seeking to create chaos is a vast one, particularly in the area of suicide bombers.
Since hijackers flew airplanes into the World Trade Center and Pentagon on Sept. 11, 2001, and the United States responded by waging wars in Afghanistan and Iraq, the number of suicide attacks have increased five-fold worldwide, said Mohammed Hafez, a political science professor and author of "Suicide Bombers in Iraq."
From the early 1980s through Sept. 11, 2001, there were 235 documented attacks, and since Sept. 12 through April 2007, there were more than 1,000, said Hafez.
In Iraq alone, a country that had not experienced such attacks previously, the 674 documented suicide bombings have outpaced those perpetrated by other groups, including Hezbollah in Lebanon, Hamas in Israel and the Tamil Tigers in Sri Lanka, Hafez said.
However, trying to diffuse "one booby trap at a time is not going to work," said Dan Kuehl, a professor at the National Defense University. In fact, the solution isn't a military one at all, but rather one of public diplomacy, he said.
The administration is working to improve its image abroad and in 2005 created a new position, undersecretary of state for public diplomacy and public affairs, which Karen Hughes now holds, to promote American values and confront supporters of terrorism.
Broad efforts include encouraging mainstream Muslim voices through ties with the Organization of Islamic Conference, and supporting financial endeavors such as long-term loans for Palestinian businesses.
Some changes in tactics have occurred as well. For instance, "for three years, the Department of Defense wouldn't let anyone appear on Al Jazeera," an Arabic television news channel, but that decision was later reversed, said Kuehl.
"If you don't engage in a medium a very large swath of your target audience listens to, that's a mistake," he said.
The United States now airs its message on satellite television and radio in an effort to slowly build an understanding and acceptance of U.S. society in the Islamic world, said Kuehl.
Efforts to reach out to moderate populations in Iraq and get their help to stop militants, such as informing U.S. troops of their activities, have proven challenging, Kuehl continued.
"That's very difficult for the United States to do because we don't have a lot of credibility with that audience," he said.
The problem, as Hafez sees it, is that Muslims view the war on terrorism as a war on Islam. The United States cast the net too widely in the war on terrorism -- all Islamic movements, even those that harbored anti-Western views, even non-violent ones, were viewed as radicals and needed to be stopped, he said.
Meanwhile, the war on Afghanistan, which many people saw as a just war, drove militants out of the country, he explained. When some militants couldn't go back home, "many of them began seeking a new haven, and when the war in Iraq broke out or appeared that it was going to break out, many of these guys saw the new frontier as being in Iraq," a territory with six borders that was easy to infiltrate, he said.
Al-Qaida, which perpetrates the bulk of the suicide attacks, is largely rejected by established Islamic movements because its members are viewed as too fanatical, said Hafez. However, even though al-Qaida takes credit for attacks, local populations still blame the presence of multinational forces and the new Iraqi government for the violence, he said.
For all of these reasons, garnering the trust of Iraqis and combating the insurgency will take time, said Kuehl, although he pointed out that some progress is being made, particularly in western Iraq, where populations are aiding or allying with the United States, or dealing with al-Qaida on their own.
But for an American public, anxious to see troops come home, waiting decades and possibly generations for a successful counterinsurgency is difficult, according to Kuehl. "We like to have nice clean wars, but counterinsurgencies are not like that."