Osama Bin Laden and his al-Qaeda network failed to carry out attacks against the United States or its allies during the war in Iraq.
Bin Laden has so far eluded US investigators
Does this mean the group is mortally wounded, or is it simply lying low and reorganising itself?
Recent arrests of senior al-Qaeda suspects have strengthened the conviction of some counter-terrorism experts that the network is in decline and disarray.
The group's failure to launch attacks during the war in Iraq is taken as proof that its organisation - and in particular its communications - have been badly damaged by a series of setbacks.
Many experts had expected al-Qaeda to take advantage of the war. And Bin Laden himself had appeared anxious to do so.
On 7 April - two days before the collapse of Saddam Hussein's statue in Baghdad - a tape purporting to be by Bin Laden urged his followers to launch suicide attacks against the US and Britain.
But nothing happened.
However, US officials are wary of sounding over confident.
Speaking before a congressional committee this week, a top FBI official, Pasquale D'Amuro, chose his words with care.
"While al-Qaeda may very well be in disarray, I believe it still has the capability to attack our interests," he said.
US President George W Bush was less cautious in his much-publicised appearance on board a US aircraft carrier last week.
Al-Qaeda suspects are being held by the US at a special camp
He declared: "The war on terror is not over, but we have seen the turning of the tide."
His speech-writers may have liked the Churchillian echo, but some commentators thought the judgement premature.
So where does the truth lie? Is al-Qaeda on the ropes? Or are the forecasts of its demise wishful thinking?
Al-Qaeda leaders, or at least those who claim to speak for them, insist they are still in business.
A man calling himself Thabet Ibn Qais, and claiming to be the group's new spokesman, told the Saudi magazine Al-Majalla that a new attack on America, on the scale of the 11 September attack, is "inevitable".
Thabet Ibn Qais was one of the companions of the Prophet Mohammed, and sometimes known as the Prophet's "voice".
In an e-mail message to the magazine, Ibn Qais said the group had reorganised its leadership, making it impenetrable to US intelligence.
In the past al-Qaeda has certainly shown great skill in adapting to new circumstances.
However, many experts question whether it is capable of launching new operations on the scale of 11 September.
Instead, they expect a persistent pattern of lower-level attacks.
Al-Qaeda has always been a loose-knit "network of networks". Groups connected to it have a good deal of local autonomy.
Even if the threat from al-Qaeda were to decline, the threat from its affiliates would remain.
As a result, governments around the world are still in pursuit of those who share its ideology - and are bracing themselves for further attacks against targets associated with the US and its allies.
Six al-Qaeda suspects arrested in Pakistan last week are believed to have been planning to crash an aircraft into the US consulate in Karachi.
Nineteen Islamic militants on the run in Saudi Arabia, following a shoot-out this week in the capital Riyadh, are described by Saudi officials as members of an al-Qaeda cell planning to carry out attacks in the kingdom.
US officials think Americans were the likely target.
The Saudi authorities found a big cache of weapons and explosives in a house the men had been using.
Many planned operations around the world have been foiled, but others may succeed.
The signs are that al-Qaeda or groups linked to it are still capable of carrying out attacks.
And its global network remains extensive, with known or suspected cells in the Middle East, Asia, Europe and North America.
The story is far from over, and many experts think the worldwide "war on terror" will remain long and arduous.
Among the uncertainties that remain is whether recent arrests will lead US investigators, as they hope, to Bin Laden himself.