Isis (Islamic State) militants are under attack on all fronts.

Soldiers and militias are pushing an offensive to dislodge the militants from Fallujah, the first major Iraqi city to fall to the group. Kurdish and Arab forces are fighting to capture the remaining stretch of Syrian territory along the Turkish border controlled by the jihadists. And in Libya, Isis' stronghold in Sirte is under pressure as militias advance from several directions.

The extremists are facing increased attacks often backed by airstrikes from a US-led coalition. But a well-resourced militant movement and the conflicting agendas of outside powers mean the group remains a powerful force.

1 Blocking the border in Syria:

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Losing control of the 70km of Syrian territory it holds along the border with Turkey would deny Isis access to a frontier it uses for smuggling weapons and fighters. The town of Manbij, northeast of strategically important Aleppo province, is at the heart of the battle, Faysal Itani, senior fellow at the Atlantic Council, said.

To Isis, Manbij represents a possible "entry point for enemies targeting the northern Aleppo countryside, and a potential staging point for a flanking operation against forces advancing on Raqqa city," the capital of the self-declared caliphate, Itani said. Losing the town would be a significant blow.

Syrian government forces are also pushing towards Raqqa, backed by Russian airstrikes, and are 30km from the Al-Tabqa military base to the city's west, according to the UK-based Syrian Observatory for Human Rights.

2 Losing ground in Iraq and Libya:

In Iraq, Fallujah lies just 50km west of Baghdad and its fall to Isis in early 2014 was a major humiliation for the Iraqi Government, one compounded by the loss of Mosul a few months later. Fallujah and nearby Ramadi, which was seized from militant control in December, are the main cities in Anbar province, home to leading Sunni tribes the Shia-dominated Government needs to rally to its side. Taking Fallujah may hasten an assault on Mosul.

European countries have been watching Isis' growth in Libya with alarm, given its proximity to Europe's southern shores and more stable North African nations such as Tunisia. Expelling the group from its foothold in Sirte would be a major relief for European leaders hit by Isis-inspired terrorism.

3 Are powers cooperating effectively against Islamic State?

Not always. American and allied planes are providing air support around Fallujah for the Iraqi military, which also benefits from the in-country help of US special forces. Iraq's powerful Shia militias are backed by Iran. The Iraqi Army and the militias cooperate, but the US and Iran have publicly ruled out working together.

Turkish soldiers frequently fire artillery at Isis forces across the border in Syria in response to rocket attacks. But Turkey is hostile to Syrian Kurdish forces, one of the most successful groups in the battlefield against Isis. Turkish officials fear that the establishment of a de facto Kurdish state on their frontier in northern Syria would embolden Turkey's own Kurdish autonomy-seeking groups, led by the PKK.

Turkey protested to the US after American special forces were photographed in action wearing insignia of the PYD Syrian Kurdish forces.

The Syrian Government of President Bashar al-Assad is supported by Russia and Iran as it battles both Isis and rebel groups. The US, European powers and Sunni Gulf monarchies demand Assad's removal in an effort to end the country's five-year war.

4 Putting Libya back together:

In Libya, Isis' stronghold in Sirte is under pressure from Petroleum Facilities Guards from the east and militias from Misrata to the west. The new United Nations-backed unity Government of Prime Minister Fayez Serraj is in the process of creating a joint command to merge the various militias that support his Administration.

But the fight against Isis will continue to include armed forces that don't support Serraj, such as those controlled by eastern commander General Khalifa Haftar who is perhaps the single biggest hurdle to reunifying fractured Libya.

Haftar has won support from neighbouring Egypt. Other countries support Serraj, but have also helped Haftar because he's got Libya's most capable armed forces. French President Francois Hollande officially backs the unity Government, but has signed major weapon deals with Egypt. Some of those "may end up in Haftar's hands," Arturo Varvelli, a research fellow at the Italian Institute for International Political Studies, wrote on May 31.

5 So, is Isis on the back-foot?

They are weaker than at the start of the year. Colonel Steve Warren, until recently a top US military spokesman, said last month that Isis has lost 45 per cent of territory it once held in Iraq and 20 per cent of that it controlled in Syria. Targeting oil infrastructure has cut the militants' production by at least 30 per cent and oil revenues by as much as 50 per cent, he said.

In Libya, Isis suffered defeats in Benghazi and was pushed from Derna by a local Islamist group.

Resistance will continue, and Isis has scored victories amid its defeats. A week into the campaign to retake Fallujah, Iraqi forces haven't penetrated the city centre. Talk about a Mosul offensive remains just that.