Abstract: We review the history of international monies and the theory related to their adoption and use. There are four key characteristics of these currencies: high unitary value; relatively low inflation rates for long periods; issuance by major economic and trading powers; and spontaneous, as opposed to planned, adoption internationally. The economic theory of the demand for money provides support for the importance of these characteristics. The value of a unit is arbitrary for a fiat money, but the other characteristics are likely to be important for determining any fiat money that will be the international money in the future. If the euro continues to exist for the next half century or so and has a relatively stable value, we conclude that the euro is likely to be serious competition for the dollar as the international money.