The Kurdistan Workers' Party (PKK) has been a thorn in Turkey's side for decades.
The PKK wants more autonomy in south-eastern Turkey
The group, which has Marxist-Leninist roots, was formed in the late 1970s and launched an armed struggle against the Turkish government in 1984, calling for an independent Kurdish state within Turkey.
Since then, more than 37,000 people have died. During the conflict, which reached a peak in the mid-1990s, thousands of villages were destroyed in the largely Kurdish south-east and east of Turkey, and hundreds of thousands of Kurds fled to cities in other parts of the country.
In the 1990s, the organisation rolled back on its demands for an independent Kurdish state, calling instead for more autonomy for the Kurds.
In 1999, it suffered a major blow when its leader, Abdullah Ocalan, was arrested.
Shortly afterwards, it introduced a five-year unilateral ceasefire and took a number of steps to try to change its image and widen its appeal, changing its name several times before deciding it again wanted to be known as the PKK.
Many Turkish soldiers have died in clashes with the PKK
It also further watered down its demands, calling on Ankara to involve it in the country's political process, allow more cultural rights for the country's estimated 15 million Kurds and release imprisoned PKK members.
There were reports of splits within the organisation.
But Turkey, which, like a number of Western countries, regards the PKK as a terrorist organisation, refused to negotiate with it and has offered only a limited amnesty to its members.
In 2004, the PKK resumed its violent campaign, which has escalated steadily over the past two years despite several other short-lived, unilateral ceasefires.
Two recent attacks - the killing of 13 Turkish soldiers in a single clash and the killing of 12 civilians in a bus ambush - were regarded as being among the worst over recent years.
Although Turkey's ruling AK Party has recently made political gains in the south-east, many Kurds, and the European Union, say the government needs to do a lot more to improve the rights of the country's Kurdish minority.
Several rebel groups swear allegiance to Ocalan
And the PKK remains popular with many people there. At the annual Kurdish spring festival, Nowruz, Kurds regularly take to the streets proclaiming their support for the group's imprisoned leader Ocalan.
A group said to be an offshoot of the PKK, calling itself the Kurdistan Freedom Falcons, has claimed responsibility for a number of bomb blasts in Istanbul and Turkish Mediterranean resorts. The group also swears allegiance to Ocalan.
And the last few years have also seen the rise of a sister organisation - Pejak - which has carried out attacks against Iran.
Turkey believes that the PKK currently has several thousand fighters based in the Candil mountains of northern Iraq; an area which is also said to be a base for Pejak.
With violence in south-eastern Turkey rising and the US and the Iraqi Kurds apparently unwilling, or unable, to take action against PKK bases in Iraqi territory, the Turkish government is now threatening to take matters into its own hands.