Northern Iraq - where at least 50 people in Irbil have been killed in a suicide bombing - has been largely autonomous since the 1991 Gulf War.
The Kurds are close allies of the US
The two main Iraqi Kurdish parties - the Patriotic Union of Kurdistan and the Kurdistan Democratic Party - have ruled the area between them, protected, for much of that time, by an international air umbrella.
Internal security has been provided by their own militia, the peshmerga.
Bayan Sami Abdul Rahman, UK representative of the Kurdistan regional government, condemned Wednesday's bombing as "a cowardly attack".
She sees it as part of a wider campaign to destabilise Iraq.
"The region is relatively safe and calm and the Kurdistan regional government has the co-operation of the public in dealing with security issues" she told the BBC.
"This is really an attempt to destabilise that, as well as part of the wider attempt to destabilise Iraq."
Bayan Sami Abdul Rahman has bitter personal experience of this kind of incident.
In February last year, her father, a prominent Iraqi Kurdish politician, was killed when suicide bombers attacked the headquarters of the two main Iraqi Kurdish parties.
However, she warned that those carrying out such attacks should not underestimate the Kurds.
"The Kurdish people have been victims of torture, of chemical bombardment, of Saddam Hussein's Anfal campaign. But every single time the Kurds have fought back," she said. "And we will fight for what we think is right - democracy, peace and prosperity for Kurdistan and Iraq."
There is no love lost between the Kurds and radical Islamist groups.
The Kurdish leaders have long been close allies of the US and are supporters of a democratic, federal, secular Iraq.
Last year, there were a string of abductions and beheadings of Kurds in areas outside the self-rule region, some of which were claimed by the Jordanian militant Islamist, Abu Musab al-Zarqawi.
In the past he has accused both the Kurds and Shias of betraying their religion.
The Kurds, long oppressed under Saddam Hussein, won the second largest bloc of seats in the new Iraqi national assembly, giving them considerable influence during the protracted negotiations on the formation of the transitional Iraqi government.
Most Kurds are anxious to retain a high level of autonomy
They have already managed to attain one of their political aims by securing a clutch of important posts, including the presidency.
However, negotiations on other crucial issues still lie ahead, as the transitional government moves to start discussing a permanent constitution for Iraq.
Perhaps the most important of these, for the Kurds, is the issue of federalism.
The Iraqi Kurdish leadership, anxious to retain a high level of autonomy in the north, is determined to push for a federal Iraqi state and wants that to be enshrined in the new, permanent, constitution.
The leadership itself is under internal pressure on this issue.
During Iraq's national elections in January, large numbers of Kurdish voters in the north also signed a separate, unofficial, petition calling for outright independence for Iraq's Kurds.