Three years on from its most deadly attacks, al-Qaeda has evolved.
There is a tendency to see it as a monolithic foe directed by an all-powerful leader pulling the strings.
But analysts believe there is a danger in laying too much emphasis on al-Qaeda and Osama Bin Laden alone when the reality is more complex - and perhaps more dangerous.
There is no doubt that the core of al-Qaeda has been disrupted. It has lost its secure sanctuary and training camps in Afghanistan and is finding it harder to organise and communicate under pressure.
The core of hardened veterans has been hit hard in the past three years.
In his New York convention speech on 2 September, 2004, President Bush declared that American strategy was succeeding and that "more than three-quarters of al-Qaeda's key members and associates have been detained or killed".
But body counts are not necessarily the most useful way of judging progress because al-Qaeda is not a "normal" military entity and the war that the US is engaged in is not a "normal" military struggle.
Interpreting the removal of al-Qaeda's key operatives as a sign of "winning" risks misunderstanding both the aims of al-Qaeda and its nature as an organisation.
Al-Qaeda affiliates are believed to be behind the Jakarta bombing
For instance, one key question is whether the organisation is recruiting new personnel faster than its current members are hunted down and whether its broader base of support is being eroded or is growing.
The focus on the core of al-Qaeda also ignores the extent to which the baton has largely passed from al-Qaeda's historic core to a broader, looser network of radical groups.
In some cases, existing insurgent groups have been radicalised through contacts with al-Qaeda and drawn into a wider network.
One example is Jemaah Islamiah in Indonesia which has increasingly attacked international targets but is relatively independent of al-Qaeda.
Other local insurgencies which were sometimes nationalist or ethnic in character have been pulled into the broader rhetoric of the war on terrorism either because of groups themselves buying into the al-Qaeda discourse of an international struggle, or because governments cracking down on them have found it useful to cast their own struggles in that wider context.
Sometimes both occur - for instance the growing Islamisation, radicalisation and internationalisation of the Chechen conflict and Russia's efforts to emphasise this trend.
The Madrid bombers seem to have been inspired by al-Qaeda
It is the local groups and affiliates, not the al-Qaeda core itself, which have undertaken most of the post 9/11 attacks.
The new, younger generation of militants may only have tenuous - if any - links to the al-Qaeda core.
The group who carried out the Madrid bombing in March 2004 were not people who had been selected, trained and were carrying out direct orders from Osama Bin Laden in the way the 9/11 hijackers had.
None of them appear to have been to Afghanistan.
Instead, they were inspired by al-Qaeda and its rhetoric and statements but seem to have operated as part of a relatively autonomous grouping of European cells.
And the more dispersed the network is - and the more it relies on local cells rather than people travelling into a country to commit an act - the harder it becomes to counter the threat because these independent actors can be harder to locate and keep track of.
Because they act so independently, getting rid of one cell does not end the problem, nor would capturing Bin Laden.
In this more dispersed structure, Bin Laden himself becomes less important as a commander issuing specific instructions and more important as an ideologue and propagandist, setting broad strategic aims but leaving local groups to decide when and how to carry out attacks.
It seems increasingly as though supporters do not wait for orders from above to carry out attacks although this does not mean that the central al-Qaeda core is no longer planning any major attacks itself - it is probably devoting its energies to try to plan a new "spectacular" attack on the US.
Bin Laden's death or capture would not end Islamic militancy
The other reason why understanding al-Qaeda's evolution is so important is because the organisation's purpose has always been as much inspirational as operational.
Attacks are a means to an end for al-Qaeda rather than an end in themselves.
Al-Qaeda's central goal is to act as a base, a kind of revolutionary vanguard, drawing as many as Muslims as possible into a broader jihadist tide of radical Islam.
This movement, they believe, would then drive the Americans from Muslim lands and overthrow governments like those of Pakistan and Saudi Arabia (which they see as propped up by the US) and lead the way for the unification of the umma - the Islamic community which would then follow what they see as a "pure" brand of Islam.
In this broader aim, al-Qaeda has had some success.
In the battle for moderate Muslims, there is no doubt that many have been alienated from the US by its invasion of Iraq and support for Israel.
The virulent ideology of violent jihad looks to be spreading.
In this sense, many experts now talk about facing a global Islamist insurgency rather than a single organisation like al-Qaeda.
However, there has not been quite the depth or breadth of embrace of radicalism that Osama Bin Laden might have wanted, and no signs yet of the tidal wave of militant Islam sweeping the Muslim world and overthrowing governments as Bin Laden had clearly hoped.
Anti-Americanism may have grown but it has not necessarily translated easily into pro-Bin Ladenism.
And so, three years on from the 11 September attacks, neither side can convincingly claim victory.
Al-Qaeda has yet to manage another major attack on the US mainland - the run-up to this November's election may show whether it is still capable of that or not given the degree of expectation among its supporters.
Whether or not this happens, it would be wrong to write off the core of al-Qaeda - its members may well still have the ability to do much damage - but it would also be dangerous to focus too much on them alone when the threat may now be broader.