We explore the impact of investors’ beliefs on cryptocurrency demand and prices using three new individual-level surveys. We find that younger individuals with lower income and education are more optimistic about the future value of cryptocurrencies, as are late investors. We then estimate the cryptocurrency demand functions using a structural model with rich heterogeneity in investors’ beliefs and preferences. To identify the model, we combine observable beliefs with an instrumental variable strategy that exploits variation in the amount of energy required for the production of the different cryptocurrencies. We find that beliefs explain a large fraction of the cross-sectional variance of returns. A counterfactual exercise shows that banning entry of late investors leads to a decrease in the price of Bitcoin by about $3,500, or approximately 30% of the price during the boom in January 2018. Late investors’ optimism alone can explain about a third of the decline.