Cryptocurrency innovations such as Bitcoin raise the question of the possible transformation of the monetary regime and how it would operate. The blockchain technology underlying Bitcoin is said to be “trustless” because it has been designed to avoid a “trusted third party.” Drawing on the institutionalist approach of Aglietta and Orléan emphasizing the importance of trust in money and the monetary system, we show that Bitcoin is characterized by: (1) methodical trust through the existence of an objective proof of payment; (2) hierarchical trust due to the concentration in the mining process; and (3) ethical trust organized around the rejection of banks and the state, although the early ethical commitment is unstable. In other words, trust is now materialized in a form of technical institution, the blockchain. However, Bitcoin cannot be used as everyday money as it would bring about a deflationist and dysfunctional monetary regime, as well as high transaction costs. Some other cryptocurrencies could lead to interesting transformations of the monetary regime if they were to provide new forms of sovereignty, avoid a design based on a fixed monetary supply, or if central banks decided to back them.