After Iraqi forces took full control of the Islamic State group's bastion of Fallujah, what's next in the battles against the extremists, not just in Iraq but in Syria and further afield?

The loss of Fallujah is the latest in a series of defeats shrinking the "caliphate" that the group proclaimed two years ago over the vast areas it conquered in Iraq and Syria in 2014.


What is the next big battle in Iraq?

Fallujah was one of only two major cities IS still held in Iraq and the security forces are now training their sights on Mosul, whose fall commanders and analysts believe would spell doom for the caliphate in Iraq.

The battle for the northern city will have different contours than previous ones, with an ever greater variety of forces than usual potentially involved in operations and staking their claim in a post-IS Mosul.

Operations aimed at retaking Mosul began months ago, with an offensive moving up the Tigris from the south and another led by Kurdish forces moving from the east, but the battle appears far from starting in earnest.


What else does IS control in Iraq?

After losing Fallujah and surrounding areas, the Iraqi half of IS's "caliphate" looks increasingly fragmented, with limited territorial contiguity between some its remaining bastions.

IS has lost the major towns and cities of Anbar but still controls the far west of the vast province, including the town of Al-Qaim near the Syrian border.

The extremists also have fixed positions in the Hamreen mountain range north of Baghdad as well as further north around Hawijah.

To the west of Mosul, IS also still holds Tal Afar, a city which was one of the first that the group took when it swept into Iraq just over two years ago.


Where are IS falling back in Syria?

On May 31, a US-backed Kurdish-Arab alliance launched a vast offensive to retake the IS stronghold on Manbij in north Syria, which lies on a key supply route for the jihadists from the Turkish border.

In around 10 days, the Syrian Democratic Forces -- who are supported by air strikes from a US-led coalition -- surrounded the city, cutting off the supply line to the extremist group's de-facto capital of Raqa city.

SDF forces have since entered the city and are edging slowly towards its centre, as IS puts up fierce resistance with suicide bombers and car bombs.

If the extremists lost Manbij, it would be their second most serious defeat since emerging in the chaos of Syria's civil war, after regime forces retook the ancient city of Palmyra from them in late March.


Is Raqa under threat?

Since late May, IS has faced two offensives in the northern province of Raqa, which the extremist group has controlled since 2014.

The SDF launched an advance from the north on May 31, but soon headed west towards Manbij in neighbouring Aleppo province.

And Russia-backed regime forces led an offensive into the province from the southwest, advancing towards the IS-held town of Tabqa. But suicide bombers drove Syrian regime troops out of the province in a lightning counter-attack last week.

Experts have said the troops backing President Bashar al-Assad in the offensive were probably not elite forces and too few to make gains in the desert area.

The provincial capital of Raqa remains the main strategic and symbolic goal for anti-IS forces, but analysts say that the extremist group's strong defences in the city mean it is unlikely to fall soon.


Can IS hold on to Sirte in Libya?

Since mid-May, Libyan pro-government forces have pressed an offensive to retake Sirte, a coastal city east of the capital Tripoli that has been under IS control since last June.

On June 9, forces loyal to the UN-backed Government of National Accord (GNA) entered Sirte, which is the only main city held by the extremist group in Libya.

They have pushed the extremists into a residential zone of just five square kilometres (two square miles) inside the city, but IS has hit back with suicide car bombs and sniper fire.