Historically, the gold standard (and sometimes a silver standard if gold was scarce or monopolized) traded places in most nations as the store of value and unit of account. These were however inconvenient to use as a medium of exchange or a standard of deferred payment due to the transport and storage concerns. Accordingly, notes began to circulate that a government or other trusted entity (e.g. the Knights Templar in Europe in the 13th century) would guarantee as representing a certain stored value on account. This was the beginning of a long slow shift to representative money.
The first historical examples of fiat money was that of China. Although paper fiat money was associated with China through the writings of Marco Polo, Chinese dynasties resorted to fiat money only in extremely desperate situations, and Chinese experiences with fiat money were that it tended to result in hyperinflation.
Until the late 20th century it was uncommon for governments to issue fiat money. In the situations where fiat money was used, it was difficult for governments to avoid the temptation of printing money which generally led to high inflation. Most modern governments limit their ability to print money by establishing independent central banks or currency boards. They are further constrained by the reactions of international currency and bond markets, which will quickly punish misbehaving governments with unfavorable exchange rates and interest rates.
The transition from the gold standard to fiat money occurred in the 1960s and 1970s. Since the end of World War II, the value of the United States dollar was pegged to 1/35 troy ounce of gold and other currencies were pegged to the U.S. dollar. This system, known as the Bretton Woods Accord, caused a massive outflow of gold in the 1960s and early 1970s. Faced by the possibility that United States gold reserves would completely disappear, President Nixon unpegged the U.S. dollar from gold on August 15, 1971.