This paper reviews what cryptocurrencies are, and it frames them within the context of historical monetary experiences and contemporary monetary economics. The paper argues that, as pure duciary private money, cryptocurrencies are a bubble without a fundamental value and that they will not provide, in general, optimal amounts of money or deliver price stability. Nevertheless, cryptocurrencies can play a role in improving the current means of payments and in disciplining central banks into providing better government-run duciary monies.