BRUSSELS — A major leap in the European Union’s digital policy and a new defense department will be two of the bloc’s top priorities for the next five years, as the new leadership and organization of its 32,000-strong executive arm was unveiled on Tuesday.

The incoming president of that executive arm, the European Commission, is Germany’s Ursula von der Leyen. She announced her team of commissioners, one from each of the 28 member states except for Britain, which is on its way out. The lineup was the commission’s most gender-balanced yet, with 12 women plus Ms. von der Leyen at the helm, alongside 14 men.

Here are the most interesting, controversial and consequential things you need to know about how the European Union will be run in the next five years.