The role of money in society has been a controversial topic in economic theory over many years. Particular attention has been devoted to the analysis whether there should be competition in the supply of money, or whether this is best left to a governmental agency. This paper reviews the theoretical literature on these issues. It also gives an overview over some episodes of free banking where banks could issue currency themselves. Finally, we highlight several aspects in which today we have competition between issuers of money, namely in the international context, with electronic money, and in large value payments systems.