Ms. Harris said Mr. Biden’s recent comments in which he waxed nostalgic about working with segregationist senators were “very hurtful,” and she criticized his opposition to busing to integrate schools in the 1970s. Read a transcript of their exchange.

The details: The progressive policy ideas that Senator Bernie Sanders has helped popularize dominated the debate, even if he did not. Here are six takeaways, as well as video highlights. We also tracked how long each candidate spoke.

News analysis: Mr. Biden’s main challenge has been presenting himself as in step with the times while turning experience to his advantage. Thursday’s debate highlighted the questions that threaten his early lead in the polls, our reporters write.

Reaction: Veteran campaign strategists and consultants on the left and the right weighed in. We also fact-checked the candidates’ claims.

From Opinion: Our columnists Jamelle Bouie, Gail Collins and Ross Douthat recapped and analyzed the evening.