Battle for Iraq and Syria in mapsContinue reading the main story
The US-led coalition has now launched more than 290 air strikes against Islamic State (IS) militant targets in Iraq, since the campaign began on 8 August.
The US, with Bahrain, Jordan, Qatar, Saudi Arabia and the United Arab Emirates, has carried out more than 180 attacks on IS in Syria since 23 September.
Separately, US forces have also carried out eight strikes against a network of al-Qaeda veterans named Khorasan who had established a safe haven west of Aleppo and were plotting imminent attacks against the West.
On 30 September, the UK launched its first air strikes against IS targets in Iraq. The attacks came four days after Parliament approved military action.
US President Barack Obama has warned his coaltion allies they are facing a "long-term campaign".
The battle for Kobane is regarded as a major test of whether the coalition's air campaign can push back IS in Syria.
Analysis of the targets hit by air strikes shows the vast majority have been IS vehicles. Lack of forces or intelligence on the ground means it has been hard to identify precise targets.Syrian oil refineries under attack
President Barack Obama vowed to dismantle the IS "network of death" and overnight on September 24, the US-led coalition targeted 12 oil refineries in Syria using fighter jets and drones.
The air strikes hit "small-scale" refineries in remote areas in the vicinity of Syrian cities such as Mayadin and Hassakeh, according to a US Central Command statement.
These refineries are believed to be producing "between 300-500 barrels of refined petroleum per day", generating as much as $2 million (£1.2m) per day for the militants, a key source of revenue for IS.
The raids carried out by US, Saudi and UAE aircraft killed 14 of the group's fighters and five civilians in eastern Syria, activists said.Mosul Dam
One of the key battlegrounds in mid-August was around the Mosul Dam - a key strategic site seized by IS fighters but subsequently re-taken by Kurdish and Iraqi forces, supported by American air attacks.
IS fighters have targeted a number of Iraqi dams during their advance, capturing the facility at Falluja in April. They went on to take Mosul in August, before US air strikes helped force them out later that month.
IS fighters have also attacked the country's second largest dam at Haditha, but the US says its strikes have cleared militants from a wide area around the facility.The rise of IS
The rapid advance of Islamic State, the extremist group that has grown out of al-Qaeda in Iraq, has thrown the region into chaos.
The Islamic State has control of large swathes of Syria and Iraq and in late June the group declared it had created a caliphate, or Islamic state, stretching from Aleppo in Syria to the province of Diyala in Iraq.
Mosul - with its Sunni Arab majority - fell after the collapse of the Iraqi security forces. Although they far outnumbered the militant fighters, many police and soldiers just abandoned their posts and fled.
Fighters had already taken the central city of Falluja and parts of nearby Ramadi in December last year.
In Syria, Islamic State militants have besieged the border town of Kobane, where they are battling Kurdish fighters. Around 140,000 residents have been forced to flee the fighting into Turkey. Airstrikes have targeted the advancing Islamic State fighters.How IS operates
Islamic State fighters - among them many foreign jihadists - have a reputation for brutality. Atrocities allegedly committed by those in the group's ranks include kidnappings, beheadings, crucifixions, torture and summary executions.
International investigators gathering evidence against Islamic State fighters have built up a detailed picture of how IS operates, with self-appointed leader Abu Bakr al-Baghdadi at the helm.
Directly beneath him are four advisory councils: Sharia (Islamic law); Shura (consultation); military and security. The latter two are the most powerful.
This one-plus-four structure is then duplicated down the chain of command to local level.Foreign fighters
The US Central Intelligence Agency believes IS may have up to 31,000 fighters in Iraq and Syria - three times as many as previously thought.
Among them are foreign recruits - the number of whom has surged since IS declared itself a caliphate in the summer, international investigators say.
Figures from the London-based International Centre for the Study of Radicalisation and Political Violence (ICSR) and the New York-based Soufan Group show an estimated 12,000 fighters from almost 80 countries have travelled to Syria and Iraq to fight with extremist groups.
The figures suggest that while about a quarter of the foreign fighters are from the West, the majority are from nearby Arab countries, such as Tunisia, Saudi Arabia and Jordan.
Some have travelled from as far away as China, Canada and Australia.
Australian officials believe at least 60 of the country's citizens are fighting with jihadist groups in Syria and northern Iraq. Others suggest the figure could be as high as 250.
On 18 September, police in Sydney arrested 15 people and charged one with conspiracy to prepare a terrorist attack following armed raids across the city.
It followed reports of a plot to carry out "demonstration killings" by Islamic extremists, including a public beheading.Establishing a caliphate
Setting up a state governed under strict Islamic law has long been a goal of many jihadists.
Based on a details posted on Twitter earlier this year, the map below shows 16 "wilayats", or provinces, that IS claims to control, or where it claims to have a presence.
The areas where IS is operating largely match areas where its predecessor, al-Qaeda in Iraq (AQI), was active during the peak of the sectarian insurgency in 2006.
AQI was eventually suppressed through a combination of a surge in US troop numbers and Sunni tribesmen taking up arms to drive it out.Refugees
About three million people have fled abroad to escape the fighting in Syria. Most have gone to Lebanon and Turkey - but a significant number have also gone to Iraq.
Syrian refugees have put pressure on local services and infrastructure in Iraq - which is also having to cope with the return of many Iraqi refugees from Syria. In addition, the UN estimates there are 1.8m Iraqis who have been forced to leave their homes to escape the conflict with IS and are now living in temporary accommodation elsewhere in the country.Ethnic and religious divide
Iraq's Sunnis are increasingly disenchanted with what they see as their systematic marginalisation by the Shia-dominated government in Baghdad and targeting by security forces.
The country is home to a range of minority religious groups who have recently found themselves caught up in the violence brought about by the rise of IS.