Accompanying Wheeler’s name and age in the Pentagon’s release was a vague description of his unit: “Headquarters U.S. Army Special Operations Command.” That phrase is a euphemism, trotted out for the 12th time since 2003 to describe a soldier killed in Iraq. The official biographies of the soldiers described in this way follow a pattern: They are old for combat soldiers, usually in their 30s. They are veterans of the Army’s elite Special Operations units — the Green Berets or, in Wheeler’s case, the 75th Ranger Regiment. And they die in known insurgent hotbeds: Qaim, Ramadi and, Thursday, Hawija.

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They are the fallen of the Army’s top-secret counterterrorist commando unit, Delta Force.

Delta has been at the heart of America’s succession of wars in Iraq — so much so that for the elite commando unit, it has been more like one long war with occasional breaks. First sent into the country in 1991 and then again in 2003, Delta left Iraq four years ago with the rest of the U.S. military. It reportedly returned last year after the Islamic State captured Mosul. It set up a headquarters for manhunting and hostage rescue missions near Irbil, the Kurdish city believed to have been the launching site for this week’s successful raid.

Delta Force’s existence, while classified, is an open secret. Former unit members thinly veil their affiliation with the Fort Bragg, N.C., unit on resumes and LinkedIn profiles with phrases such as “Special Mission Unit” and “Army Compartmented Element.” Memoirs describe training that molds veteran soldiers — and a few Marines — into “operators” who can work with little advance planning in active combat zones and postwar chaos alike, sometimes blasting into compounds with attack dogs barking and guns blazing and sometimes going unnoticed altogether.

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Although overshadowed in recent years by its Navy counterpart, SEAL Team 6, Delta has hardly flown under the radar. Chuck Norris starred in the action flick “The Delta Force” in 1986, when Delta was less than a decade old, and the unit’s “D-Boys” were made famous by the book and movie “Black Hawk Down,” about the 1993 Mogadishu battle in which five operators were killed and two received posthumous Medals of Honor for their courage in the face of near-certain death.

This fall’s blockbuster “Sicario” gives Delta an aesthetic update familiar to anyone who has encountered operators in America’s post-Sept. 11 wars: hulking physiques, snub-nosed carbines rife with high-tech attachments, civilian clothes mixed with MultiCam fatigues, and the bushy beards that have been de rigueur since commandos first started growing them in Afghanistan in 2001.

Delta’s exploits have spanned the globe, from Colombia, where Delta operators helped track down cocaine kingpin Pablo Escobar, to Afghanistan, where Delta launched its first big helicopter assault less than six weeks after Sept. 11 and later waged a several-year campaign around the northern city of Kunduz, to Libya, where two operators’ heroics during the controversial 2012 battle of Benghazi earned them the military’s second-highest valor awards.

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Iraq, though, has been the centerpiece. The first three Delta soldiers known to have died on operations were killed in a helicopter crash while hunting Iraqi Scud missiles in 1991, and of the 23 operators lost in the field since then, Iraq has claimed 12.

Famously credited by the U.S. general who oversaw Operation Desert Storm with keeping Israel from entering the 1991 war by keeping a lid on Iraqi Scud attacks, Delta went home when the shooting stopped. But according to journalist Sean Naylor’s explosive new history of American special operations, “Relentless Strike,” undercover Delta personnel returned to Iraq routinely during the ensuing decade as part of United Nations weapons inspection teams.

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Delta operators reprised their 1991 role during the 2003 invasion of Iraq, roaming the western desert in specially outfitted vehicles and then taking on the hunt for Saddam Hussein and his loyalists. But it was the rise of al-Qaeda in Iraq, the terrorist group from which today’s Islamic State group is descended, that threw Delta into its longest, toughest campaign, the one this week’s rescue mission in Hawija is arguably an extension of.

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Delta fought in Iraq as long as American troops were there, hammering al-Qaeda in Iraq with nocturnal raids that occurred just out of sight of the embedded reporters who covered the overt war.

In a vivid passage in his memoir “My Share of the Task,” retired Gen. Stanley McChrystal, who oversaw Delta teams for years in Iraq, describes accompanying Delta operators on a raid in Fallujah that barely missed Abu Musab al-Zarqawi, al-Qaeda in Iraq’s founder and the ideological godfather of the Islamic State. (McChrystal uses the common euphemism “Task Force Green.”) Delta operators racked up valor awards for their bravery, but the toll was heavy. Six operators died during one three-month mission on the border with Syria in 2005, the worst toll for the unit since Mogadishu.

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Early in his book, McChrystal describes his decision, in 2003, to commit Delta to the fight against terrorists in Iraq on a near-permanent basis (again using the euphemism “Green”). “My guidance was simple,” McChrystal writes: “Green would be in charge [in Iraq] until we won.”

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Eventually, it seemed like Delta had won. When Zarqawi was eventually killed, it was a Delta commander who gave the order, and Delta operators who retrieved the terrorist leader’s corpse. And in secret memos described in Michael Gordon and Bernard Trainor’s Iraq War history “The Endgame,” Gen. David Petraeus credits Delta and its sister units with an outsize role in the success of the “surge,” the U.S. counteroffensive that decimated al-Qaeda in Iraq’s leadership and sent its remnants into hiding.

When the U.S. military pulled out of Iraq at the end of 2011, it did so with its head held high, and Delta went with it — even though, according to one Special Operations officer, the unit maintained contingency plans until the bitter end to keep a stay-behind force in the country.

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The rise of the Islamic State from the ruins of al-Qaeda in Iraq ended Delta’s hiatus from the country that has claimed more of its members than any other. Until Friday, when Sergeant Wheeler’s death was announced, Delta’s renewed role in the country was mostly a matter of speculation, although convincing reporting has attributed two risky raids into Syria to Delta.

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This time, the base of operations is not Baghdad or Anbar, where Delta fought hardest last time around, but Irbil, the city that acts as the staging base for the Kurdish war against the Islamic State in the northern Iraq. Delta’s ties to Kurdish security forces also run deep.

The most highly regarded Kurdish counterterrorist unit was formed in Delta’s image with the help of “the guys from Bragg,” as a Kurdish commando recently put it to a Special Operations veteran reporting from Iraq. When Kurdish troops apprehended the al-Qaeda operative Hassan Ghul, who under interrogation provided one of the clues that eventually led the CIA to Osama bin Laden, they turned him over to Delta operators, according to a blog post by a Delta commander-turned-novelist involved in the mission.

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In another way, Delta’s latest bout in Iraq is a return to its roots, and a vindication of its original purpose. Although the unit’s forte for the past two decades has been manhunting, it was formed in 1979 as a hostage rescue team, and blooded in the disastrous Eagle Claw rescue mission that failed to retrieve American hostages from Iran. Hostage rescue missions in the interim have been few and far between, vastly outnumbered by “kill/capture raids.”