The debate began cordially but turned caustic. Mrs. Clinton called Mr. Trump a “puppet” of Russia, and he called her a “nasty woman.”

Here are highlights of the debate.

• European Union leaders gather again in Brussels today, in part to seek a common position on Russia. Some officials want to impose new sanctions because of its bombing of Aleppo, Syria. Italy, meanwhile, is reported to have insisted on discussing whether to ease sanctions imposed on Moscow over the war in Ukraine.

The 28 leaders will also discuss a free-trade pact with Canada, which has faced stiff opposition.

One has become known for his fashionable scarves. Another is never far from his country’s nuclear codes, even at briefings. Here’s a look at the style and substance of some of the European politicians meeting today.