Today's tax systems, in which value-added taxes and payroll taxes play a prominent role, are largely creations of the 1950s. We need to invent modern tax systems adapted to the reality of the 21st century: the growing importance of capital and the rise of inequality. This article reviews some of the challenges involved with increasing the progressivity of tax systems in a globalised world and discusses how these challenges could be overcome. I make the case for new and more ambitious forms of international cooperation and for modern forms of wealth taxation.