There are numerous reports of foreign jihadists going to Somalia to help al-Shabab.
It has imposed a strict version of Sharia law in areas under its control, including stoning to death women accused of adultery and amputating the hands of thieves.
Al-Shabab At A Glance
- "The Youth" in Arabic
- Formed as a radical offshoot of the Union of Islamic Courts in 2006
- Affiliated to al-Qaeda
- Killed 76 people in double attack in Uganda during 2010 football World Cup
- Estimated to have 7,000 to 9,000 fighters
In August, it announced a "tactical withdrawal" from the capital, Mogadishu, after a sustained offensive by African Union (AU) and government forces.
The AU and the government claimed that al-Shabab had been routed in the capital.
However, in early October, a suicide bomber detonated a lorry-load of explosives near a government building, killing more than 70 people.
Analysts believe al-Shabab is increasingly focusing on guerrilla warfare to counter the firepower of AU forces.
Kismayo, a port city, is a key asset for the militants, allowing supplies to reach areas under their control and providing taxes for their operations.
In September, the US launched a series of attacks by unmanned drones on suspected al-Shabab positions around Kismayo.
There have been reports - strenuously denied by al-Shabab - that his leadership is being increasingly challenged by southerners, who form the bulk of the group's fighters, estimated to number between 7,000 and 9,000.
Mr Godane is rarely seen in public. His predecessor, Moalim Aden Hashi Ayro, was killed in a US airstrike in 2008.
In its most public confirmation of the links, al-Shabab officials accompanied a man claiming to be from al-Qaeda and identified as US citizen Abu Abdulla Almuhajir as he distributed aid to famine victims in Islamist-controlled territory.
US officials believe that with al-Qaeda on the retreat in Afghanistan and Pakistan following the killing of Osama bin Laden, its fighters will increasingly take refuge in Somalia.
The attack was carried out because Uganda - along with Burundi - provide the bulk of the 9,000 AU troops in Somalia.
Neighbouring Djibouti and the western African state of Sierra Leone have promised to bolster the AU force to 12,000 by the end of 2011.
Kenya said it had sent troops to Somalia because al-Shabab fighters had abducted two Spanish aid workers from the world's largest refugee camp, Dadaab.
Al-Shabab has denied responsibility.
Analysts say the militants often enter and leave Kenya without being intercepted. Their fighters are said to even visit the capital, Nairobi, for medical treatment.
The 2002 twin attacks on Israeli targets near the Kenyan resort of Mombasa were allegedly planned in Somalia by an al-Qaeda cell, while the US believes some of the al-Qaeda operatives who carried out the 1998 attacks on its embassies in Nairobi and Dar es Salaam then fled to Somalia.
Eritrea supports al-Shabab to counter the influence of Ethiopia, its bitter enemy.
With the backing of the US, Ethiopia sent troops to Somalia in 2006 to defeat the Islamists. The Ethiopian forces withdrew in 2009 after suffering heavy casualties.
It was hoped that he would be able to achieve peace with al-Shabab, but the group simply denounced him as a traitor and a puppet of foreign powers.
Somalia is pretty much a failed state. It has not had an effective national government for about 20 years, during which much of the country has been a constant war-zone.
This made it easy for al-Shabab, when it first emerged, to win support among Somalis. It promised people security - something they welcomed.
But the on-going fighting has knocked al-Shabab's credibility.
The group advocates the Saudi-inspired Wahhabi version of Islam, while most Somalis are Sufis. Al-Shabab has destroyed a large number of Sufi shrines, causing its popularity to further plummet.
And al-Shabab is battling to deal with a famine in six areas under its control. Tens of thousands of people have fled its territory in search of food to government-controlled territory and to neighbouring Kenya and Ethiopia.
Al-Shabab acknowledges there is a drought, but denies that it amounts to a famine.
It has refused to allow the UN World Food Programme (WFP) and several Western agencies from distributing aid in areas under its control, accusing them of having a political agenda.
One of the famine-affected areas is Lower Shabelle. It was once Somlalia's breadbasket, but years of fighting forced farmers to flee.
A-Shabab blames the lack of rains on Allah, and says people should pray for the drought to end.
It has also urged people to return to their villages to plant crops, rather than becoming dependent on aid.