Ms. Warren said that her ideas were the only ones ambitious enough to attract enough voter support to defeat President Trump. Here are six takeaways and video highlights from the debate.

Joe Biden defended his son Hunter’s overseas work, but the former vice president otherwise kept a lower profile.

And Senator Bernie Sanders tried to reassure voters of his stamina two weeks after a heart attack. He, Mr. Biden and Ms. Warren, all of whom are in their 70s, were asked about their age.

Reaction: Experts on the left and the right weighed in. We also fact-checked the candidates’ claims and tracked how long each one spoke.

From Opinion: Our columnists and contributors ranked each candidate’s performance.

The Daily: Today’s episode is about the debate.