And Christine Lagarde, the French managing director of the International Monetary Fund, will lead the European Central Bank.

Von der Leyen: A medical doctor and economist by training, she is likely to bring a fervor for more European integration. She has said she wants a “United States of Europe,” a goal that could prove difficult. She will also deal with the chaos surrounding Brexit.

Lagarde: She was the first chairwoman of the Chicago-based law firm Baker McKenzie, and the first woman to become finance minister of a Group of 8 economy. And she is surely the first central banker who was a competitive synchronized swimmer.

Her legacy at the I.M.F. includes the fund’s largest bailout, a $57 billion deal with Argentina credited with averting a default. Read our profile of her here.

Other new leaders: Charles Michel, the acting prime minister of Belgium, will serve as the European Council president. At 43, he is among the youngest European leaders, though he grew up surrounded by politics. He is known for being a deft coalition-builder.