The main aim of this article is to explain how a computer process, the «Blockchain» or chain of blocks, can generate the necessary trust for the creation, acceptance and increasingly widespread use of digital currencies, under a new concept or paradigm of money not maintained by any state or supranational entity: cryptocurrencies. In order to understand this process, the technical aspects of how the blockchain operates and how it has managed to generate confidence in the end user are explained first. Secondly, its implementation will be analyzed through the best known of all, Bitcoin, and through the data related to the expansion and use of the main cryptocurrencies in a market that in the last two years has multiplied by 65, reaching half a trillion dollars. This work closes by exposing the main conclusions and reflections.