The invention of digital ledger technology, the creation of private digital currencies and central banks’ ongoing projects to create public digital money (CBDC) raise fundamental economic questions regarding the nature, features and functions of money. This SUERF BAFFI Bocconi e-Lecture on “Conceptions of Money in the Digital Age” brings together leading experts in the field to discuss key issues, based on economic principles against the background of various conceptions of money during the history of economic thought. The aim is to get a better grip on our understanding of the options and the choices to be made in the design of private and public digital money, and the consequences arising from such choices.