The Union of Islamic Courts controlled most of southern Somalia for six months after winning a battle for the capital, Mogadishu, in June.
The US say they are linked to terrorist groups but they deny that.
Who are they?
Somalia has not had a proper government for 16 years. Instead, warlords have been fighting for control of territory.
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Local Islamic courts were set up by businessmen who wanted someone to catch and punish thieves and people who do not respect their contracts.
Some of these courts joined to form the Union of Islamic Courts (UIC) and their small groups of gunmen became Somalia's strongest fighting force.
What do they want?
The UIC is divided between moderates and hardliners.
They all say they want to restore stability and law and order to Somalia.
Hardliners also want to curb foreign influences, which they say are immoral. They have closed down cinemas showing foreign films and football matches.
Some radio stations have also been told not to play foreign music or local love songs but other radio stations and cinemas have been left alone.
The UIC have also staged public executions and floggings of people they have found guilty of crimes such as murder and selling drugs.
Are they popular?
After years of lawlessness, many Somalis are happy to have some kind of law and order.
The prices of many basic foods have fallen because gunmen no longer extort money from lorries taking goods to markets.
Almost all Somalis are Muslim but some are wary of the hardline elements.
They do not like the harsh punishments and do not want to be cut off from the rest of the world.
What about other countries?
The US and Somalia's big neighbour Ethiopia do not like the UIC - one of the UIC hardline leaders is on a US list of people linked to terrorism.
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The UIC deny these accusations.
The United Nations recognises Somalia's transitional government which was set up in 2004 after two years of peace talks.
But before the large-scale Ethiopian intervention in December 2006, the interim government controlled only a small piece of territory around the town of Baidoa.
Ethiopia's rival, Eritrea, is accused of passing weapons to the UIC.
There have been fears a major regional war in Somalia, with Ethiopia and government forces battling the UIC, backed up by Eritrea and Islamist fighters from around the world.