As the world's reserve currency, the dollar gives Washington a powerful influence over global financial markets -- a point underlined again this week when a record fine was levelled against France's leading bank.
French banking giant BNP Paribas has agreed to pay $8.9 billion (6.5 billion euros) to US authorities for violating sanctions against Iran, Sudan and other countries even though the transactions were not illegal under French or European law.
It fell foul of US rules because the exchanges were carried out in dollars, and the huge penalty has sent shockwaves across Europe where other major banks such as Credit Agricole, Deutsche Bank and UniCredit fear they could be next in the cross-hairs of the US authorities.
For some, it is a sign that Europe must wean itself off the dollar.
"The global reach of American standards through the use of the dollar should push Europe to boost the euro as an international exchange currency," French Finance Minister Michel Sapin said after the fine was announced.
US authorities were able to catch BNP's embargo violations by monitoring clearing houses for large interbank transactions.
Every time a transaction is made in dollars -- wherever it takes place -- it must pass through a computer "clearing" system intended to guarantee its security.
That gives Washington huge scope to monitor the financial activities of anyone using the dollar and identify cases like that of BNP.
Jerome Sgard, a professor at Paris's Sciences Po university, says the BNP Paribas case shows how Washington is using the dollar's reach to extend its political influence.
"What is new is the crossover between the financial and the judicial," he said.
- 'Our currency, your problem' -
For decades, the dollar has been the bedrock of the world's financial system.
Oil and commodities are overwhelmingly traded in dollars, as are big ticket items like planes -- and not just when deals are done between US companies and their partners.
European aircraft maker Airbus sells its planes in dollars, and when Russia and China signed a mega gas deal in May, they chose the US currency as well.
Among other advantages, trading in dollars reduces the number of foreign exchange transactions and makes it easier to compare prices.
In 1964, then-French finance minister Valery Giscard d'Estaing noted that the US enjoyed an "exorbitant privilege" because of the dollar's dominant role in the international monetary system.
Washington's enormous advantage is that it can run up almost limitless debt in its own currency.
That was underscored in 1971 by then US Treasury secretary John Connally. Speaking to European counterparts worried about exchange rates, he quipped: "The dollar may be our currency, but it's your problem."
In 40 years, not much has changed.
According to the International Monetary Fund, 61.2 percent of known reserves in central banks around the world were held in dollars at the end of last year.
In April 2013, the greenback was also used in almost nine tenths of all foreign exchange transactions, according to the Bank for International Settlements.
- Yuan's rise -
Some countries have tried to free themselves from the supervision implicit in using the greenback.
Iran has decided to accept gold and other currencies in exchange for its oil in a bid to circumvent US sanctions, while aeronautical sector specialists say mixed payments for planes are becoming more common.
China, the world's second-largest economy after the US, is also promoting the greater use of its currency overseas to boost its own international status.
Beijing last year started to exchange the yuan directly against the Japanese yen, and announced the creation of clearing houses for its currency in several European countries and Australia.
On Friday China's central bank said it had also designated a clearing bank in Seoul for yuan transactions in South Korea.
But Beijing -- which does not want too strong a yuan since that would make its exports less competitive on international markets -- is keeping a close eye on the trades.
"We have heard a lot of talk about paying for oil in yuan, or for Airbus planes in euros, but it is not becoming a trend," Sgard noted.
For there to be a real change in the international money hierarchy, he said, there would need to be "a systemic rupture" like the two world wars that curbed the role of the British pound.