The invention of blockchain technology has radically changed the perception of how monetary systems can be structured and operated. Central banks and state authorities mostly refuse to acknowledge that cryptocurrencies are money, yet the number of payment transactions using cryptocurrencies is increasing and cryptocurrencies form a non-negligible stake of wealth. As with other economic phenomena, cryptocurrencies shall be addressed in the financial statements of the entities using them, albeit without any accounting guidance in current financial reporting standards. This paper fills this void by suggesting, comparing, and assessing potential accounting models under IFRS. Based on evidence from literature review, as well as recent time-series data on the price volatility of cryptocurrencies, the paper shows that fair value accounting is the most relevant source of useful information for users of financial statements when cryptocurrencies are acquired for investment purposes. Furthermore, the paper identifies scenarios under which cryptocurrencies shall be treated as (foreign) currencies, even though financial system regulators do not consider cryptocurrencies as being money (fiat currency).