BBC Middle East analyst Roger Hardy has spent the last two months investigating Wahhabism, Saudi Arabia's austere brand of Islam.
In the first of a two-part series, to be broadcast on the BBC World Service, he looks at the fierce debate over whether Wahhabism and Saudi petrodollars have fomented extremism.
"The essence of Wahhabism is purity," says Lawrence Wright, author of a Pulitzer-prize-winning book about al-Qaeda.
Saudis feature heavily among those accused of anti-US terrorism
"They are only interested in purification - and that's what makes them so repressive."
Prince Turki al-Faisal, the former head of Saudi intelligence and former ambassador in London and Washington, dismisses the accusation out of hand.
"From our point of view in the kingdom, there is no such thing as Wahhabism. That's a canard."
Saudis have never cared for the "Wahhabi" label which historically was a term of abuse applied to them by their critics.
They are highly sensitive to the charge that they have used their vast oil wealth to turn an obscure desert sect into a global force.
Charge and counter-charge
Over the last two months I've talked to officials of the Saudi government and Saudi charities who argue the campaign against them is unjust.
I've heard some of the world's leading experts, gathered in a small town in the Dutch countryside, attempt to define Wahhabism - and Salafism, the bigger family of conservative Sunni Islam of which it's part.
I've heard senior US investigators describe their deep-rooted suspicions about Saudi charities - and the frustrations of following the money trail.
Top US attorney Patrick Fitzgerald told me why he'd come to believe a Saudi charity headquartered in Chicago was an al-Qaeda front.
The US authorities shut down the charity, the Benevolence Foundation, in 2002.
Two years later another major Saudi charity, al-Haramain, came under scrutiny.
The US and Saudi governments designated 10 of its branches "financiers of terrorism".
But American investigators have often found it hard to turn suspicion into proof.
And that reinforces the scepticism of Saudi and American Muslims about US government claims.
I looked at the role of Wahhabi literature - used in Saudi schools and exported round the world - in promoting suspicion and hatred of non-believers.
The Saudi ambassador in Washington, Adel Jubeir, assured me a series of steps had been taken to reform the country's educational system to instil values of tolerance.
Saudi educationalist Hassan al-Maliki remains to be convinced.
"They are teaching the students," he told me, "that whoever disagrees with Wahhabism is either an infidel or a deviant - and should repent or be killed."
This, he added, was an attack on half of Saudi society, where Shia and Sufi minorities coexist uneasily with the dominant Wahhabi religious establishment.
I visited the offices of the World Assembly of Muslim Youth (Wamy), part of the global network of well-funded Islamic institutions created by Saudi Arabia's King Faisal in the 1960s and 1970s.
These bodies built mosques and schools and provided humanitarian aid to Muslims in need.
But there is evidence that, over time, some of their local branches became involved in militant networks.
Bernard Haykel, professor of Near East studies at Princeton, believes the Saudis set in motion a process over which they lost control.
The Saudis' funding of militant Islam reached a new pitch in the 1980s when, with the United States and others, they bankrolled the jihad against Soviet troops occupying Afghanistan.
The Afghan war was the crucible from which emerged al-Qaeda.
"The genie came out of the bottle," says Professor Haykel, "and the Saudis could no longer put it back in."
The first of Roger Hardy's programmes, Jihad & the Petrodollar, can be heard on the BBC World Service on Friday, 16 November.