Policy-makers are struggling to accommodate cryptocurrencies within tax systems not designed to handle them; this paper reviews the issues that arise. The greatest challenges are for implementation: crypto’s pseudonymity is an inherent obstacle to third-party reporting. Design problems arise from cryptocurrencies’ dual nature as investment assets and means of payment: more straightforward is a compelling case for corrective taxation of carbon-intensive mining. Ownership is highly concentrated at the top, but many crypto investors have only moderate incomes. The capital gains tax revenue at stake worldwide may be in the tens of billions of dollars, but the more profound risks may ultimately be for VAT/sales taxes.