By Frank Gardner
Security correspondent, BBC News
Saudi Arabia's King Abdullah arrived in the UK on Monday for the first state visit by a Saudi monarch for 20 years.
The Saudi flags are flying along the road to Buckingham Palace
He will be the guest of Queen Elizabeth II at Buckingham Palace and is due to meet British political leaders on Wednesday, culminating in a glittering state banquet.
The visit is the product of years of patient diplomacy and is an indication of how Saudi Arabia has become one of the UK's closest allies in the Middle East.
On Monday five planes touched down in the UK, bearing the octogenarian King Abdullah and an entourage of Saudi ministers, businessmen and journalists.
Saudi Arabia and the UK clearly matter to each other, with the relationship going well beyond trade, although last year British commercial exports to Riyadh exceeded £3.5bn.
Around 20,000 Britons live and work in Saudi Arabia and the UK has now landed a massive export order for the Typhoon fighter jet.
This has not been without controversy. In 2006 this multi-billion pound order appeared to be at risk of cancellation as the UK's Serious Fraud Office (SFO) threatened to probe into the private Swiss bank accounts of Saudi princes as part of their investigation into alleged corruption in Saudi-UK arms deals dating back to the 1980s.
The Saudi monarchy also indicated that if the probe went ahead then co-operation between the two countries on counter-terrorism would cease.
Tony Blair, who was prime minister at the time, stopped the probe, triggering an outcry by anti-corruption campaigners in the UK and Europe.
This week both British and Saudi officials are hoping this issue will not overshadow the packed agenda.
On Monday the so-called Two Kingdoms Dialogue will be opened by speeches from the British Foreign Secretary, David Miliband, and the Saudi Foreign Minister, Prince Saud al-Faisal.
The UK-Saudi relationship was strong during Tony Blair's term
The UK Foreign Office says the conference will focus on youth, education and cultural dialogue. But underpinning the Saudi-UK relationship is a large and growing bilateral trade and ever closer diplomatic and security co-operation on trying to resolve the flashpoints of the Middle East.
King Abdullah's 2002 peace initiative for the Palestinian-Israeli dispute is still the only peace plan on the table, and behind the scenes Saudi Arabia has been working to calm tensions in Lebanon and to find ways of resolving the insurgency in Iraq.
But one of the Saudis' prime concerns today is how to contain their giant neighbour Iran and its suspect nuclear programme.
So sensitive is this issue that King Abdullah declined to discuss it in a recent interview with the BBC, so this week's visit is unlikely to see any new announcements in that area.
Sport, education and even double taxation are all on the agenda this week.
There is also a three-day exhibition of photographs at the Victoria & Albert Museum in London of rare photographs from Princess Alice's visit to the Saudi kingdom in the 1930s.
Beyond all this, say officials, the Saudis will be hoping to correct some of the misconceptions that have arisen about their country since 15 Saudi nationals took part in the 9/11 attacks on New York and Washington in 2001.
A UK deal to sell Typhoon fighter to Riyadh has been controversial
Initially the Saudi ruling family publicly denied they had a problem with violent religious extremism but they faced a devastating wake-up call in May 2003 when al-Qaeda carried out a triple suicide bombing in Riyadh that killed over 30 people.
Since then they have removed or "retrained" extremist preachers and reformed much of the educational curriculum, excising extremist tracts that encouraged intolerance and even violence towards non-Muslims.
They have also embarked on a widescale public information campaign to steer young Saudis away from violent jihad.
But with conflict raging in neighbouring Iraq, the Palestinian issue still unresolved and thousands of Western troops deployed to the region - where they are often seen as "occupiers" - there are still many recruits to al-Qaeda's cause.
King Abdullah has told the BBC it will take 20 to 30 years to defeat terrorism.
Despite close Anglo-Saudi co-operation on security and intelligence the Saudi leadership maintains that it passed the UK information that might have averted the London bombings of 2005 if it had been acted on.
Whitehall officials have strenuously denied this, and a subsequent investigation by the UK Parliament's Intelligence and Security Committee (ISC) found no evidence of any actionable intelligence passed by the Saudis that could have prevented the 7/7 bombings.