Does Awwad Ibrahim Ali al-Badri al-Samarrai, better known by his nom de guerre, Abu Bakr al-Baghdadi, have cause to worry? A crude allies-versus-adversaries tally would suggest he does. But appearances can be deceptive. The Islamic State (IS), of which Baghdadi is the Amir al-Mu’minin (Commander of the Faithful), has taken some hits lately, but it’s in no danger of being knocked out.

The array of foes that IS faces is certainly formidable. And they are coalescing to destroy the Caliphate Baghdadi and his acolytes have created in swaths of Syria and Iraq. The United States, Britain, France, Australia, Jordan, Saudi Arabia, Qatar, the United Arab Emirates, Turkey, Iran, and Russia have come to agree that the Caliphate must be put out of commission. The Kurds of Syria, Iraq, and Turkey agree.

Together, these states and communities possess formidable resources. The United States alone has reportedly spent nearly $9 million a day since starting its anti-IS air campaign last fall.

The United States, Saudi Arabia, the UAE, and Turkey are bombing IS’s bastions in Syria. American, British, French, and Australian warplanes are doing so in Iraq. Jordan’s jets have struck IS sites in both Syria and Iraq.

Aside from this combined air campaign, the Caliphate is under attack on the ground. Shiite militias trained and equipped by Iran, and attached to the Hashd al-Shaabi (Popular Mobilization Forces) collective, have pushed northward into its Sunni-majority territories, as has the U.S.-backed Iraqi army. Kurdish fighters from Syria (the YKP, People’s Defense Units) and Iraq, and more intermittently from Turkey, have moved against its northern flank.

IS has suffered some significant setbacks as a result. Kurdish fighters (Syrian as well as Iraqi) have expelled its forces from Kobane (aka Ayn al-Arab) and Tal Abyad, adjacent to the Turkish border. In Iraq, IS soldiers have been driven from Tikrit, a Sunni stronghold and source of oil wealth, which also happens to be Saddam Hussein’s birthplace. Though the Caliphate continues to hold Mosul, Iraq’s second biggest city, which it seized in June 2014, it forfeited the Mosul dam two months later.

If nothing else, these reversals punctured the aura of invincibility that the image-obsessed, media savvy Caliphate has created and used as a tool for recruitment and sowing fear. Though IS embraces a Salafist-inspired doctrine rooted in an idealized conception of Arabia’s 7th century Islamic community, it runs a 21st century, Internet-driven, PR machine.

Despite its losses, IS’s destruction is scarcely imminent. Though damaged, it retains important sources of strength and resilience, even appeal.

To begin with, unlike al-Qaeda, it has by any reasonable definition established a state. With its capital in Raqqa, Syria, and a population of about eight million, the Caliphate extends from northwestern Syria to the western approaches of Baghdad and protrudes northward toward the boundaries of Iraqi Kurdistan. Estimates of its size range from 11,000 square miles (equivalent to Belgium) to an implausible 81,000 square miles (approximating Britain minus Northern Ireland), the variance depending on what’s counted: populated lands in Syria and Iraq, or those plus uninhabited terrain in these two countries and the dozen or so other places further afield where militant Islamist groups have aligned with IS. But even the smaller approximation is impressive given that IS emerged only in 2013 and Baghdadi proclaimed his Caliphate a little more than a year ago.

IS has also created governing institutions, central and provincial, that run the gamut. Shari’a law is interpreted and enforced (aided by blood-chilling forms of punishment). Taxes are collected. Schooling—based on Wahhabi precepts—is provided, as are various social services. Intelligence is gathered, soldiers recruited and trained. An apparatus of horror is tasked with kidnappings, beheadings and forced amputations, mass atrocities, and sexual slavery—all justified by bizarre theological pronouncements.

But the Caliphate would never have achieved what it has were it led by a small band of sociopaths that relied solely on brutality to extract obedience. There’s more to IS than its horrendous cruelties would suggest. In anarchic, violent Syria and Iraq, it has acquired a social base by providing people—more precisely, those who adhere to its draconian theological rules, don’t rebel, and refrain from aiding and abetting its enemies—security, functional institutions, and basic economic necessities. Many of those living under IS rule doubtless have no choice, but others are drawn to its mission of building an Islamic polity and restoring the pieties and glories of old.

Successful state-creation explains in part why IS attracts followers from numerous countries, many of whom defy the stereotype of jihadist converts as lost souls: anomie-ridden, marginalized, poorly educated, and professionally unsuccessful. The commitment to re-creating a transnational Caliphate also accounts for the oaths of fealty (bayat) that IS has garnered from Islamist groups extending from Pakistan to Libya and even southward to Nigeria.

IS has other sources of strength. Its operations are funded by multiple sources of income, including taxes, revenue from selling natural resources, ransoms and cash from shadowy Persian Gulf sources. Its fighters, well-armed, battle-hardened true believers, have acquitted themselves well against enemies with larger numbers and better weapons.

In short, the Caliphate isn’t an itinerant terrorist center with embryonic cells strewn across the world. That’s one of the reasons it has eclipsed al-Qaeda.

Yes, airstrikes can damage IS, and already have, by killing its leaders, destroying its political infrastructure, and disrupting its capacity to deliver day-to-day public services.

Destroying IS, which President Obama has vowed to do, is another matter. Despite its retreats from Kobane, Tal Abyad, and Tikrit, IS has advanced elsewhere, including Ramadi, in Iraq’s Anbar province (and less than 100 miles west of Baghdad), and the ancient Syrian town of Palmyra, both of which it overran in May.

While the Pentagon estimates that the Caliphate now controls a third less territory in Iraq than it did a year ago, such statistics may not have lasting significance in what is bound to be a prolonged seesaw war waged on multiple fronts. Demolishing, rather than degrading, the Caliphate will require well-trained, well-armed ground troops capable of shrinking its territorial base and undercutting its social support.

This raises the question of how effective Iranian-backed Shiites militias, Hezbollah (which is fighting in Syria), Kurdish forces, and troops controlled by an exclusionary Shia-dominated Baghdad government will prove in a long war with IS, whose base is overwhelmingly Sunni Arab.

The local forces fighting IS bring a lot of political baggage to the battlefield—this in a part of the world that in recent years has witnessed massive violence between Shiites and Sunni Arabs and clashes between Arabs and Kurds. Added to this is the historic legacy of strife between Arabs and Turks and Arabs and Persians that still hangs heavy. No amount of American firepower can negate these disadvantages.

As for the possibility of deploying Western troops, after the multi-year wars in Iraq and Afghanistan, Americans, to say nothing of Europeans, have no stomach for yet another protracted war in Muslim lands, particularly in light of how these two counterinsurgency-cum-nation building ventures have turned out.

The resulting impediment to intervention is a good thing. It is well to remember that IS emerged from Al Qaeda in Iraq (its leadership remains mainly Iraqi), which itself was nourished by the (continuing) frenzy of Sunni-Shia violence that followed the American-designed 2003 invasion of Iraq. One of the lessons of that war remains relevant to the current debate on what to do about the Caliphate: hubris produced by the sense of military invincibility can trigger decisions, the calamitous consequences of which reach far into the future.

The justification offered for using American military power against the Caliphate is that it poses a serious threat to the United States. Unlike al-Qaeda, however, IS has directed its venom and violence primarily, though certainly not exclusively, against those Muslims it condemns through takfir (the judgment of apostasy), above all Shiites.

Yes, it has been unspeakably cruel toward various Christian peoples and other religious minorities, notably the Yazidis. Allowing for the element of sadism, the main impulse for this is the obsession with building a Caliphate based on its puritanical brand of Islam. Yes, it has beheaded Westerners and other foreigners, but only in retaliation for airstrikes and to advertise its reputation for mercilessness, not in service of a war against the West. Though these are shocking, reprehensible acts, IS’s focus has been on creating, consolidating, and expanding a Salafi Caliphate in Syria and Iraq, not orchestrating a Huntingtonian clash of civilizations.

Should the United States nevertheless worry about terrorism inspired, even directed, by IS? Not so much, aver some experts, insisting that the warnings about this danger amount to “hype.” They point out that relatively few Americans have rushed to join the Caliphate’s wars and that there’s no evidence that those who have are being groomed to return home and stage terrorist attacks.

Perhaps so, but many Europeans—those born as Muslims as well as converts—have been mesmerized by the IS’s narrative of sacrifice, apocalypse, salvation, and Utopia. Because millions of people travel yearly from Europe to the United States, there can be no watertight distinction between Europe’s security from terrorism and America’s. Experts have the leeway to opine that the chances of an IS terrorist attack in the United States are minimal, but no responsible American government can base its planning and policy on such breezy projections.