The real fear for the future since the attacks in New York and Washington is that dozens, perhaps hundreds of operatives loyal to Al'Qaeda are in America and Canada ready to strike again, awaiting a call from Osama Bin Laden.
Al'Qaeda, or The Base, also has supporters in almost every European country and active cells in 34 nations.
In every terrorist act by Al'Qaeda since the early 1990s bin Laden has ensured that the actual suicide bombers were "sleepers", long-time residents of the countries they attacked, with ordinary jobs, identity papers and a social and family life. Bin Laden has spent a decade building up such networks of individuals, some of whom have never travelled to Afghanistan to meet him.
A Pakistani official said: "Bombing Afghanistan and bin Laden will just be lopping off the top of the tree, it will not be taking out all the branches, which are everywhere."
Building up such a network has required money, weapons and secure sanctuaries and staging areas, which bin Laden has acquired only because the West has ignored the civil war in Afghanistan for a decade.
Bin Laden set up Al'Qaeda in Peshawar, Pakistan, in the late 1980s as a welfare organisation to pay pensions to the widows and orphans of Arabs who had died while fighting Soviet troops alongside the Afghan Mujaheddin.
It expanded as bin Laden set up businesses, training schools and money laundering rings in Afghanistan, Pakistan, Sudan and the Middle East.
He also had the resources of his wealthy family, the largest construction magnates in Saudi Arabia. His personal wealth was estimated by the CIA at £160 million, although much of that was frozen by America after Al'Qaeda bombed two US embassies in Africa in 1998.
Since then bin Laden has raised funds by drugs trafficking from Afghanistan and smuggling consumer goods from Dubai and other ports in the Arabian Gulf to Iran, Pakistan and Central Asia.
Bin Laden has also ignored the world banking system in favour of "hundi". For decades, millions of migrant workers from the Indian subcontinent who work in the Arab states use Pakistani and Indian money lenders to send earnings home.
Last year Pakistan's State Bank received about £540 million in remittances from the country's migrant workers. Hundi delivered an estimated £2 billion. It is an informal system, which uses chits of paper, telephone calls and word of mouth.
Workers in the Gulf hand over their earnings to money lenders, who phone their agents scattered in towns and villages in the home country, who in turn deliver the same sum to the families of the workers.
Hundi is now operating in America, Canada and Britain, and bin Laden has tapped into this risk-free system. The US attacks were likely to have been funded through hundi.
Afghanistan and the Taliban have provided extraordinary facilities not available anywhere in the shadowy world of international terrorism. Thousands of Al'Qaeda recruits spend six months of the year fighting for the Taliban, gaining battle experience and training in the use of weapons and explosives.
Since 1998, bin Laden has used fax, telephone and e-mail connections from Pakistan rather than Afghanistan, as satellite communications in Afghanistan are too closely monitored by the CIA.
Al'Qaeda is an umbrella organisation that now includes dozens of militant groups from around the Muslim world. Bin Laden provides funds, training facilities in Afghanistan and overall direction, but he does not necessarily provide daily control. Instead, these groups, such as the 20 Algerians arrested in Europe this summer, have their own agendas, which are not necessarily communicated to bin Laden, unless there are big operations such as the American attacks.
By distancing himself from these sub-groups, bin Laden has confidently been able to deny responsibility for every act of terrorism he has carried out, even though he has always praised the perpetrators, just as he has denied involvement in the American attacks but praised the suicide bombers.
Ahmed Rashid is the author of The Taliban, Islam, Oil and the New Great Game in Central Asia, published by IB Tauris.