The move marks a new phase in operations that had so far focused on clearing areas around Fallujah, a city west of Baghdad that looms large in the Islamic State group's mythology.
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Here are five essential facts about Fallujah:
1) Rebel city
Fallujah was once a small trading post on the Euphrates River, 50 kilometres (30 miles) west of Baghdad, but its aura in modern Iraq belies its relatively modest size.
Sunni tribes were always powerful in Fallujah, whose reputation as a troublesome city predates the US-led invasion of 2003.
In 1920, the murder there of a British officer was one of the sparks that ignited a nationwide revolt against the colonial power.
The anti-British rebellion was the inspiration for the name of an armed group called the 1920 Revolution Brigades, which was founded in 2003 and still active in the Fallujah area in 2014 before it was swallowed up by IS.
2) 'City of Mosques'
Fallujah is an important religious hub for Iraq's Sunni minority. Its skyline bristles with hundreds of minarets that have earned it the nickname "City of Mosques".
Built on a crossroads for routes from Saudi Arabia and Jordan, Fallujah was one of the first places in Iraq where hardline Wahhabi ideology took root.
Now executed dictator Saddam Hussein jailed several radical preachers from Fallujah, although the city was generally not hostile to him and benefited from the policies of his Baath party regime that favoured Sunni Arabs.
3) Blackwater Bridge
On March 31, 2003, insurgents ambushed a convoy carrying four US contractors working for the private military company Blackwater. They were killed, their bodies dragged on the road and eventually hung from a bridge over the Euphrates.
Photos of the mutilated bodies were beamed around the world, and remain among the most searing images of the US-led war in Iraq.
The bridge became known as "Blackwater Bridge" and the incident jolted the world into an awareness of the violent reality that was going to prevail in Iraq, a year after the overthrow of Saddam.
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4) 'New Vietnam'
Operation Phantom Fury was launched on November 7, 2004 and turned into the bloodiest battle US service personnel had seen since the Vietnam War.
They went house to house in a bid to retake a city that had already become the capital of Al-Qaeda in Iraq, a precursor of the Islamic State group that was founded by Abu Musab al-Zarqawi.
The battle, in which 95 US troops were killed and more than 500 wounded, holds a special place in recent US military history. Varying estimates put the number of insurgents killed at between 1,000 and 1,500, and civilian casualties were believed to be in the hundreds.
5) 'Head of the snake'
Fallujah fell to anti-government fighters in early 2014 after security forces withdrew during unrest that began when they cleared a year-old anti-government protest camp near Ramadi, the capital of Anbar province, sparking fighting that later spread to Fallujah.
The fall of the Fallujah, which later became a key IS stronghold, was the first time that anti-government forces had exercised such open control in an Iraqi city since the height of the violence that followed the US-led invasion.
IS's broad offensive, in which second city Mosul was captured, did not happen until June 2014.
Fallujah is seen by many Iraqis as the place where it all began and is sometimes nicknamed "the head of the snake".
