In the short term, probably very little. King Fahd had been on the throne since 1982, but suffered a series of debilitating strokes in 1995. Since then Crown Prince (now King) Abdullah, Fahd's half-brother, has in practice run the country. Thus the sons of the kingdom's founder King Abdel-Aziz remain in charge.
Abdullah has sought a balance between cautious reform and tackling terrorism. That strategy is likely to remain the same. However, Abdullah is believed to be marginally less pro-Western than his predecessor, whose most significant single decision was to allow US forces to be based on Saudi soil in 1990, when an invasion by Iraq was widely feared.
Now he is king in name as well as deed, he may shift the focus towards closer ties with other Arab states. Nonetheless, the alliance with the US and the West, based on mutual interests of oil and security, will remain the bedrock of Saudi foreign policy.
What will be the impact on the oil market?
Again, very limited, despite the small jump in crude prices after the news of Fahd's death. Saudi Arabia remains the world's largest exporter. It is likely to continue trying to prevent excessive market swings. But the recent surge in prices has been a windfall, allowing the country to press ahead with economic changes andreduce its dependence on oil (which accounts for 45 per cent of Saudi GDP).
What about terrorism?
The presence of "infidel" American troops in the country that guards the holiest shrines of Islam was one of the most powerful grievances voiced by Osama bin Laden. Over the past two years, Saudi Arabia (where 15 of the 11 September hijackers originated) has suffered a series of al-Qa'ida attacks targeting Saudis and expatriate workers. The Saudis claim to have captured or killed 23 of the 26 most wanted terrorists. But although there has been no major recent attack, no one believes the threat is over.
Who is Abdullah's successor?
Prince Sultan, 77, and a full brother of the late King Fahd, was named as crown prince.He is currently defence minister and a deputy prime minister. His power base is the army and he has long been a strong supporter of the US alliance. His son, Prince Bandar, was the influential Saudi ambassador in Washington for two decades until he resigned in July. Another of Sultan's sons, Prince Khalid, commanded Arab forces in the 1991 Gulf war. But the Sultan's age and fragile health - he had an operation for stomach cancer in 2004 -means his tenure may be relatively brief. Real change in Saudi Arabia may have to await the passing of the generational torch.