The Tawhid and Jihad group has claimed responsibility for numerous suicide bomb attacks in Iraq since Saddam Hussein's regime was toppled.
Zarqawi himself is believed to have killed some of the hostages
It has also been behind the kidnapping and beheading of foreign civilians linked to the US, including Briton Kenneth Bigley.
Gruesome videos showing the final moments of their victims' lives are often released.
The group is said to be led by Abu-Musab al-Zarqawi.
Imprisoned in Jordan during the early 1990s, Zarqawi has become Iraq's most-wanted man.
He has been linked with both al-Qaeda and the Ansar al-Islam movement in northern Iraq.
The US says that many attacks, including the killing of nearly 200 Shia worshippers celebrating the religious festival of Ashura in bombings in Karbala and Baghdad, bear the hallmarks of operations planned by Zarqawi.
Reward for capture
The US has vowed to capture Zarqawi, offering a $25m reward for information leading to his death or capture.
Although some sources describe the Zarqawi group and Tawhid and Jihad as separate entities, internet postings and video footage suggest that Zarqawi is in charge.
The ideology of Al-Tawhid wa al-Jihad, whose name means Unity and Jihad, seems to be similar to that of al-Qaeda, but with a focus on Iraq.
An extremist, fundamentalist Sunni group, it sees itself as engaged in a struggle against American "crusaders", contrasting the strict monotheism of Islam to the "polytheist" Christian Trinity.
They perceive the invasion of Iraq as a step towards a Greater Israel, and reject Shia Muslims as "al-Rafidah" or rejectionists. They view the Kurds as enemies, partly because of their alleged links with Jewish interests.
Tawhid and Jihad justify the beheading of foreign hostages with the Koranic verses that are hotly contested by many Muslim scholars.
The group is thought to have only a few hundred members, but is considered very dangerous.
Paul Bremer, the former administrator of the Coalition Provisional Authority, believed Tawhid and Jihad members were responsible for almost all the suicide attacks in Iraq.
Though the authorities have captured some members, Mr Bremer said: "They have a cellular structure, so information does not flow widely. It makes it difficult to penetrate. Even if you do penetrate, you do not get much information beyond the cell."
In May 2004, Tawhid and Jihad announced it had joined forces with another Islamist organisation, the Salafiah al-Mujahidiah group of Abu-Dajanah al-Iraqi.
Since then, the group has claimed responsibility for the killing of Izzedin Salim, the chairman of the dissolved Governing Council of Iraq, as well as several other members of the interim administration.
The group has also threatened to kill Prime Minister Iyad Allawi.
Suicide bombings and attacks on oil installations, Iraqi police and National Guard facilities have continued unabated.