After Iraqi forces took full control of the Islamic State group's bastion of Fallujah, what's next in the battles against the jihadists, 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 jihadists 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 jihadist 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 jihadists 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 jihadist 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 jihadist 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 jihadist group in Libya.

They have pushed the jihadists 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.

Cities and towns retaken from IS in Iraq and Syria
Baghdad (AFP) June 26, 2016 - Iraqi commanders announced the complete recapture of key Islamic State group stronghold Fallujah on Sunday after declaring victory in the city a week earlier.

Here is a recap of key cities and towns retaken from IS in Iraq and neighbouring Syria:

Iraq

FALLUJAH: Anbar province's second city and one of IS's most emblematic bastions in the country, located just 50 kilometres (30 miles) from Baghdad. It was seized by anti-government fighters in 2014 and later became a key IS stronghold.

While the battle has been won, Iraq still faces a major humanitarian crisis in its aftermath, with tens of thousands of people who fled the fighting desperately in need of assistance in the searing summer heat.

RAMADI: The capital of Anbar, the country's largest province that stretches from the borders with Syria, Jordan and Saudi Arabia to just west of the capital.

IS seized Ramadi, located 100 kilometres (60 miles) west of Baghdad, in May 2015 in an assault involving dozens of suicide bombers driving explosives-rigged vehicles. Iraqi forces launched an operation to retake the city late last year and declared full control over the area earlier this year.

TIKRIT: Hometown of late Iraqi dictator Saddam Hussein located 160 kilometres (100 miles) north of Baghdad, it was the second city after Mosul to fall to IS. It was recaptured in April 2015 by Iraqi troops, police and Shiite-dominated paramilitaries. The operation, which was at that time the largest by Iraqi forces against IS, was helped by the fact that much of Tikrit's civilian population had fled the city.

SINJAR: Iraqi Kurdish forces backed by US-led coalition air strikes recaptured Sinjar, 400 kilometres (250 miles) northwest of Baghdad, from IS last November. That cut a key supply line linking areas held by the jihadists in Iraq and Syria. IS captured Sinjar in August 2014 and carried out a brutal campaign against its Yazidi minority that included massacres, enslavement and rape.

BAIJI: Iraqi forces recaptured the town of Baiji, 200 kilometres (120 miles) north of Baghdad in October 2015.

Baiji and the country's largest refinery, located nearby, were the scenes of some of the longest-running battles with IS in Iraq. The town lies at a major crossroads and its recapture was seen as key to preparing the ground for offensives in Anbar and Mosul, the last major Iraqi city held by IS.

Syria

PALMYRA: Known as the "Pearl of the Desert", Palmyra was overrun by IS in May 2015, after which the jihadists blew up UNESCO-listed temples and looted ancient relics.

Syrian regime forces backed by Russian warplanes and allied militia retook the ancient city from IS in March this year.

KOBANE: A Kurdish town in northern Syria on the Turkish border. It became a symbol of the fight against IS, and the jihadists were driven out of Kobane in January 2015 after more than four months of fierce fighting with Kurdish forces backed by US-led strikes.

The city, known in Arabic as Ain al-Arab, is the capital of one of three semi-autonomous "cantons" established by Kurds after the Syrian war erupted.

TAL ABYAD: Another city on the Turkish border, it was captured by Kurds in June 2015. Tal Abyad lies on a key supply route between Turkey and IS stronghold Raqa, and jihadist fighters and arms regularly passed through the city before its recapture.