Convertibility is the quality that allows money or other financial instruments to be converted into other liquid stores of value. Convertibility is an important factor in international trade, where instruments valued in different currencies must be exchanged.
Currency trading 
Freely convertible currencies have immediate value on the foreign exchange market, and few restrictions on the manner and amount that can be traded for another currency. Free convertibility is a major feature of a hard currency.
Some countries pass laws restricting the legal exchange rates of their currencies, or requiring permits to exchange more than a certain amount. Some currencies, such as the North Korean won, the Transnistrian ruble and the Cuban national peso, are officially nonconvertible and can only be exchanged on the black market. If an official exchange rate is set, its value on the black market is often lower.
Convertibility controls may be introduced as part of an overall monetary policy. For example, restrictions on the Argentine peso were introduced during an economic crisis in the 1990s, and scrapped in 2002 during a subsequent crisis.
Commodity money 
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Convertibility first became an issue of significance during the time banknotes began to replace commodity money in the money supply. Under the gold and silver standards, notes were redeemable for coin at face value, though often failing banks and governments would overextend their reserves.
Historically, the banknote has followed a common or very similar pattern in the western nations. Originally decentralized and issued from various independent banks, it was gradually brought under state control and became a monopoly privilege of the central banks. In the process, the fact that the banknote was merely a substitute for the real commodity money (gold and silver) was gradually lost sight of.
Under the gold exchange standard, for example the Bretton Woods Institutions, banks of issue were obliged to redeem their currencies in gold bullion, or in United States dollars, which in turn were redeemable in gold bullion at an official rate of $35 per troy ounce. Due to limited growth in the supply of gold reserves, during a time of great inflation of the dollar supply, the United States eventually abandoned the gold exchange standard and thus bullion convertibility in 1974.
Under the contemporary international currency regimes, all currencies' inherent value derives from fiat, thus there is no longer any thing (gold or other tangible store of value) for which paper notes can be redeemed.