There may also have been disagreement within the group about the announcement in February 2012 of an alliance between Al-Shabaab and al Qaeda and about the group's ban on foreign aid organizations working in Somalia to save millions threatened by famine.
How and from where does it recruit?
The organization has a sophisticated public relations arm that includes a Twitter account and video production abilities.
"Remember Mumbai?" one tweet asked Saturday, as gunfire was erupting from Westgate mall in Nairobi. The comment was an apparent reference to the 2008 attack in which 10 Pakistani men associated with the terrorist group Lashkar-e-Tayyiba stormed several buildings in Mumbai, India, killing 164 people over a three-day period.
"Some youngsters resist death even when told not to be taken alive. It's going to be a long ordeal," Saturday's tweet said.
Soon after, it announced it was responsible for Saturday's attack in Nairobi, Kenya. "Alshabab confirms its behind the #Westgate spectacle," it said.
A 2009 Al-Shabaab video is as slickly produced as a reality TV show, complete with a hip-hop jihad voice and a startling message.
"Mortar by mortar, shell by shell, only going to stop when I send them to hell," an unidentified voice raps on the video in American English.
The video shows a man reported to have been Abu Mansoor al-Amriki, a U.S. citizen from Alabama. "Away from your family, away from our friends, away from ice, candy bars, all those things is because we're waiting to meet the enemy," he says.
But enemies -- and alliances -- can shift.
Al-Amriki, whose real name is Omar Hammami, said last year in a video posted online that he had had a fallout with Al-Shabaab "regarding matters of the sharia and matters of strategy" and feared for his life. He was reported last week to have been killed in Somalia by Al-Shabaab. CNN is not able to confirm the report.
Finding replacements may not be hard.
Sheikh Ahmed Matan, a member of Britain's Somali community, said he knows of hundreds of young Somali men living in the West who returned to Somalia for terrorist training.
How is it funded?
The once ragtag Somalia-based al Qaeda affiliate has grown into an economic powerhouse, raising tens of millions of dollars in cash from schemes that have involved extortion, illegal taxation and other "fees," according to the 2011 United Nations report.
The United States believed then that the group was coordinating with al Qaeda groups in Yemen and might have been plotting attacks in the region and abroad.
In 2011, it was generating "between $70 million and $100 million per year, from duties and fees levied at airports and seaports, taxes on goods and services, taxes in kind on domestic produce, 'jihad contributions,' checkpoints and various forms of extortion justified in terms of religious obligation," according to the report from the U.N. Monitoring Group on Somalia and Eritrea.
How have Somalis been affected?
Years of lawlessness and poverty have exacted a toll that Al-Shabaab has not helped. In 2011, the United Nations declared a famine in the southern Somalia regions of Bakool and Lower Shabelle, and Al-Shabaab reversed an earlier pledge to allow aid agencies to provide food in famine-stricken areas.
That year, the U.N. Interagency Group for Child Mortality Estimation announced that Somalia had the highest mortality rate for children 4 and younger in the world.
In May, a report jointly commissioned by the U.N. Food and Agriculture Organization and the USAID-funded Famine Early Warning Systems Network reported that 258,000 Somalis had died in the famine between October 2010 and April 2012 and that half of the victims were younger than five.
What is the United States doing?
The United States has supported U.N.-backed African forces fighting Al-Shabaab and strengthened its counterterrorism efforts against the group.
It has also donated millions in aid.
The U.S. State Department said this week that Somali security forces, aided by the African Union Mission in Somalia, have driven Al-Shabaab out of major cities and towns, creating "a window of opportunity to fundamentally change Somalia's trajectory.