The Islamic State, a terrorist organization that once ran a fiefdom across the heart of the Middle East as large as the United Kingdom, is now a largely decentralized and homeless movement of ideologies, criminals, and social misfits. In the 10 months since ISIS lost control of the last sliver of its caliphate in the plains of Eastern Syria, its fighters have transformed into a band of insurgents taking potshots at Iraqi and Syrian government troops and associated militias.  

ISIS may be down but it’s not out. The Iraqi-Syrian border remains highly porous, which provides the militants with the space to move back and forth with relative ease. The group continues to recruit, even if their social media presence is a far cry from the past. As Mike Giglio and Kathy Gilsinan wrote in the Atlantic, “Even after America spent billions of dollars during two presidencies to defeat ISIS, deployed troops across Iraq and Syria, and dropped thousands of bombs, ISIS persists.”

But it’s important to keep a cool head when we read alarmist reports about ISIS conducting attacks in Iraq at a heightened pace. You can find the “ISIS is newly resurgent” narrative in a lot of news stories, U.N. Security Council reports, and Pentagon documents. But all of them need to be digested in their proper context—a context that is often buried under a pile of popular myths about terrorism in general and ISIS in particular.

Myth #1: Kill the leader and watch the group fall

You can call this the terrorism version of the Drug Enforcement Administration’s Kingpin strategy: arrest or wack the guy at the top and watch as his sycophants, loyalists, and middlemen collapse. If only counterterrorism was that simple. 

Killing a senior leader of a terrorist organization is enormously satisfying. Remember when President George W. Bush held a June 2006 news conference in the Rose Garden to announce the killing of Al-Qaeda in Iraq chief Abu Musab al-Zarqawi? Or the jubilant crowds chanting “USA, USA!” outside the White House gates in 2011 after President Barack Obama broke the news about Al-Qaeda founder Osama Bin Laden’s death in a daring Seal Team 6 raid in Pakistan? Or the pride Trump felt at the podium when he told the world that  Abu Bakr al-Baghdadi “died like a dog?”

Each operation was a personal achievement in its own right, but the groups continued to operate after the leader was taken off the field. Zarqawi’s AQI morphed into ISIS, while Bin Laden’s Al-Qaeda is still in business. ISIS didn’t fade with the death of its founder.  As the Defense Department Inspector General on the counter-ISIS campaign concluded last month, “USCENTCOM and the

DIA both assessed that the October death of al Baghdadi did not result in any immediate degradation to ISIS’s capabilities.”  While decapitation can help throw a movement into confusion (Israel’s campaign against Hamas helped decrease the number of lethal attacks against Israeli civilians), they aren’t a magic panacea.

Myth #2: The more territory ISIS controls, the more terrorism there is against America

The safe-haven hypothesis is deeply ingrained in the terrorism field. So it was with ISIS, where the group’s hold on territory in 2014 created panic in Washington (understandable from where U.S. officials were sitting at the time) that attacks on the United States were more likely. In the Islamic State’s case, however, the caliphate-building project in Iraq and Syria took priority over external operations. Constructing a medieval, religious-based entity across state borders and doing everything to keep that entity running smoothly—collecting taxes; resolving petty disputes, passing laws; enforcing order; providing basic services to the population; deterring internal enemies; maintaining a support base or at least maintaining dominance through intimidation; enlisting soldiers—is painfully hard work that requires significant attention and resources. 

If anything, external attacks put this entire project at risk. ISIS learned this through first-hand experience after beheading Western journalists on videotape and enslaving ethnic minorities in northwestern Iraq—both of which inspired the United States to assemble a military coalition against the group. The ISIS caliphate’s years-long annihilation came on the back of stupid mistakes. 

Ironically, with the caliphate destroyed, ISIS can now spend less resources on running a bureaucracy and more on running operations.

Myth #3: ISIS can be defeated

One of the most fundamental misconceptions about terrorism, in general, is that a final victory against these groups is possible. The Bush, Obama, and Trump administrations continue to talk about terrorism as a threat that can be eradicated from the face of the earth when such a goal is physically impossible to achieve. The word “defeat” is a terribly counterproductive one to use in the terrorism context, for it suggests that killing every last terrorist on the planet or pressuring a terrorist group to sign some surrender document is not only doable but viable. In reality, “winning” (another word that should be generally avoided) the war against ISIS in the traditional sense is about as likely as winning the war on drugs, crime, or poverty: it’s nice to think about, but so is climbing Mt. Everest in a day.

Terrorism is an ever-changing, ever-amorphous, often faceless threat. Groups constantly evolve their tactics and strategies, shift their goals, re-brand if it suits their interests, lay low when the military pressure becomes unmanageable, and exploit opportunities when they come. Terrorism has been around since the beginning of civilization, and it will, unfortunately, be with us until the end of it. The job of counterterrorism professionals is how best to contain it.

Daniel DePetris is a fellow at Defense Priorities, a foreign policy organization focused on promoting a realistic grand strategy to ensure American security and prosperity.