The US dollar plays a dominant role in the invoicing of international trade, albeit not an exclusive one as more than half of global trade is invoiced in other currencies. Of particular interest are the euro, with a large role, and the renminbi, with a rising role. These two currencies are well suited to contrast the roles of economic fundamentals and policies, as European policy makers have taken a neutral stance in contrast to the promotion of the international role of the renminbi by the Chinese authorities. We assess the drivers of in- voicing using the most recent and comprehensive data set for 115 countries over 1999-2019. We find that standard mechanisms that foster use of a large economy's currency predicted by theory|i.e. strategic complementarities in price setting and integration in cross-border value chains|underpin use of the dollar and the euro for trade with the United States and the euro area. These mechanisms also support the role of the dollar, but not the euro, in trade between non-US and non-euro area countries, making the dollar the globally dominant invoicing currency. Fundamentals and policies have played a contrasted role for the use of the renminbi. We find that China's integration into global trade has further strengthened the dominant status of the dollar at the expense of the euro. At the same time, the establishment of currency swap lines by the People's Bank of China has been associated with increases in renminbi invoicing, with an adverse effect on dollar use that is larger than for the euro.