There are nations that do not have an official currency of their own. Instead they use stable currencies of other nations such as the Australian dollar, the Swiss franc, the US dollar or the euro. The idea behind it is to avoid the adverse effects of economic and political developments at home such as steep inflation which can deter investment. Additionally, it helps avoid the exchange rate risks.
Acceptance of another nation’s currency as its own, also requires nations to relinquish control over money supply and bank interest rates. And it is highly unlikely that the nation whose currency is being used will factor in the needs of others while determining interest rates. These are the pitfalls of not having a currency of one’s own. To make up, such nations depend on taxes and spending to stoke their economies.
The US dollar, so far, has seen maximum uptake by nations because of its stability and widespread acceptance in global trade. Besides sovereign countries, there are unincorporated territories controlled by the US by dint of being closer to it such as Puerto Rico, Guam, Samoa and Northern Marianna Islands that use the US dollar. Insular territory of the US such, namely the Virgin Islands also uses it.
This slideshow sheds light on the dollarized nations in the world and what drove them to such a decision.