Hamas's biggest backer? It has the entire Westin the palm of its hand
The Queen with Qatar’s former ruler, Sheikh Hamad bin Khalifa Al-Thani
the complex politics of the Middle East. The country's control of an estimated 14 per cent of the world's known reserves of natural gas has allowed it to buy itself a seat at the top tables of global diplomacy.
The way in which Qatar allegedly bribed and cajoled its way into hosting the Fifa World Cup in 2018 is well documented but so far has done little to force a change of heart at the highest level of football.
Similarly, the country's quixotic foreign policy has so far failed to dislodge its special relationship with the West.
Qatar's young ruler, Sheikh Tamim bin Hamad Al Thani (who displaced his father a year ago), has thrust himself into the vortex of Israel's struggle against Hamas. Qatar manages the remarkable feat of being a diplomatic and military ally of the United States while being the only Gulf state to be an open supporter of Hamas.
In the Syrian civil war, Qatar was an early supporter of some of the jihadi groups fighting President Bashar al-Assad's regime. Those outfits transformed themselves into the Islamic State, a bloodthirsty collective that has torn apart Iraq.
The cash flow
Amount given to Gaza by Qatar in 2012 for "road building" projects
Percentage of global natural gas supply controlled by Qatar
Estimated value of Qatar Investment Authority's UK assets
Amount paid by Qatar's state fund for Harrods department store
Qatar's role as a supporter of rebel movements is all the more remarkable given the US's war on terror, in place since the 9/11 atrocities in 2001, and the global effort by the Americans to impose sanctions on all those who deal with terrorist organisations.
The rulers of Qatar won the confidence of Nato during the first Iraq war of 1999-2000, when Saddam Hussein invaded Kuwait, and in the American-led 2003 invasion of the country. On both occasions, the West pre-positioned troops and munitions in Qatar.
The Americans still maintain a presence in the country at the Al Udeid Air Base west of Doha.
The country has also won friends in diplomatic circles and among the Western public for the way in which its broadcaster, Al Jazeera, has established itself as one of the few credible news sources in Arab lands.
Throughout the recent conflict, Qatar has studiously interviewed Israeli spokesmen, including cabinet ministers. Some neutrals claim that it has given a more independent view of events than the BBC.
The Gulf state's reach into the heart of the British establishment was underlined this year at the Royal Ascot. The Qataris sponsored the most prestigious event in British racing through their investment company Qipo, and the Emir of Qatar accompanied the Queen as she made her way down the racecourse to the Royal enclosure on the first day of the meeting.
Qatar likes to see itself as the champion of the Arab underdog. It was in this capacity that it was one of the few Arab states to support the deposed Muslim Brotherhood in Egypt and has funnelled financial support to Hamas.
In 2012, the Emir's father provided $254 million in assistance to Gaza to support road building projects.
More recently, it has been reported that Qatar transferred large sums to an Arab bank to pay the salaries of the 55,000 Hamas civil servants who found their wages cut off after the June 2014 unity agreement between Fatah and Hamas.
Qatar's other pet diplomatic projects have included seed money for a fund to protect the Arab nature of East Jerusalem. It offered $250m as the down payment on a $1bn fund.
Qatar's support for the Muslim Brotherhood and Hamas has led to a major rift with other Gulf states. In March 2014, the ambassadors from Saudi Arabia, Bahrain and the UAE were recalled from Qatar because of its recognition of the Brotherhood - regarded as a terrorist movement elsewhere in the Gulf.
Despite Qatar's curious enchantment with radical politics and its open support for Hamas, there has been no shortage of British businesses willing to accept Qatari cash. The best known symbol of its power and influence in London is the Harrods department store, bought from the Egyptian Al-Fayad family in May 2010 for £1.5 bn.
That is just the tip of an iceberg of Qatari funds flowing into London.
The London Stock Exchange is 15 per cent owned by the Qatari Investment Authority. Qatar Holdings is a 26 per cent shareholder in the £6 billion J Sainsbury group and is seen as a potential future owner.
Qatari investors have been hugely active in British property. At the height of the financial crisis, Qatar stepped in to bail out the Shard in London. It partnered Delancy estates in redeveloping the Olympic Park and financed the Candy Brothers in developing One Hyde Park. Qatari investors own the Chelsea Barracks site in West London and a huge development off Oxford Street in conjunction with Land Securities.
Their property speculations have aroused some hackles. The attempts to win control of three prestigious London hotels - Claridges, the Connaught and the Berkeley - have brought them head to head against the owners of the Daily Telegraph group, the Barclay Brothers. They have expressed private concerns that Qatar, a state so closely involved with terrorism, should be allowed to own London hostelries.
Qatar caused a stir in France when it bought Paris Saint-Germain football club in 2011 and proceeded to turn it into a contender for the Champions League, buying up top players from around the world.
So far, Qatar appears to have bought itself Western protection. But how it can continue to support terror and the countries that abhor it, is one of the great strategic puzzles of our time.
Alex Brummer is City Editor of the Daily Mail