What is a fiat currency?
First of all, fiat according to the Oxford dictionary, means a formal authorization or proposition.
While currency is any form of money that is accepted as a medium of exchange and is currently in circulation. (See definitions of money and medium of exchange in the FAQ section at the bottom of this page)

Chao, the world’s first paper currency (China)
Now, currency is ANY form of money.
So, currency includes both:
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Money that carries only putative value such as paper money
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AND money that carries naturally-existing value such as silver and gold coins
Therefore, unlike many think, currency does not automatically mean paper money.
What is a fiat currency exactly?
Now, to put the two words together…
A fiat currency is basically when something with no intrinsic value and not backed up by any asset is made to be used as a medium of exchange (money) by a government order.
Past
A fiat currency is not something that has been around only for the last couple hundred years.
In fact, the first recorded fiat currency made of paper, chao, is over 750 years old. It was introduced in 1260s during the Yuan dynasty.
In the past the majority of fiat currencies were made of paper. Those that were not made of paper were made from easily-accessible and cheap metals (such as iron and copper).
In general, in the past, many surprising and unexpected, at least for those living in the 21st century, items were used as currencies.
For example, seashells and salt. These items hold very little value today. However, in ancient times, seashells were limited in supply by long travels to the seaside. While salt wasn’t easy to find or extract from the ground.
Today
Today, first of all, the majority of currencies are fiat.
Second, all of them are made of paper.
In fact, today there are over 170 fiat paper currencies in the world.

Zimbabwe dollar collapsed in April of 2009
Now, since money with putative value is a fiat currency… That makes money with naturally-existing value to be a non-fiat currency. The difference between the two is huge.
Fiat currency is used only in geographical regions where it is agreed to be used by the governing bodies.
- For example, pound sterling is officially only used in United Kingdom and several small Crown-dependent regions.
While non-fiat currency, because it contains an internal value, is accepted everywhere.
- For example, gold, is accepted in 194 nations around the world.

Cleaning up Hungarian streets. Hungarian pengo turned out to be useless after its collapse in 1946
It has a tendency to fail, sooner or later
Throughout history, more than 600 fiat currencies were used by various nations.
They share one aspect in common. All of them went through devaluation and eventually collapsed.
Based on the number of years each existed, the average life expectancy of a fiat currency is 27 years.
Why it fails
Any fiat currency fails, earlier or later, because, backed up by nothing, there is no intrinsic value to it.
The value of fiat currency is purely determined by:
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supply
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the amount of it available at any given time
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demand and
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the desire of people to use it
Now, a fiat currency doesn’t fail because of lack of supply. Because let’s face it, the amount of paper available to print the currency is basically unlimited.
The real reason behind its failure is lack of demand.
People eventually lose trust in something that is available in unlimited amounts and at any time can be doubled or tripled in circulation.
This is exactly what happened with Zimbabwe dollar in 2009, Swedish krona in 1992 and Hungarian pengo in 1946.
Conclusion
As a summary and to put it straight a fiat currency is ‘made-up’ money with artificially created value and, unfortunately, its collapse is inevitable.
Your opinion and questions are welcome — leave them below.
Main references:
www.investopedia.com
www.naturalnews.com
www.oxforddictionaries.com
www.wikepedia.com
www.investorwords.com
www.thesovereigninvestor.com
FAQ
A fiat currency is basically when something with no intrinsic value or not backed up by any asset is made to be used as a medium of exchange (aka money) by a government order.
Money is any item or record that is accepted as a payment for goods and services. It must be a medium of exchange, unit of account (be measurable) and store value over time.
The instance when something is used as an intermediate when exchanging goods and services, it functions as a medium of exchange.