A slimmed-down Democratic debate dominated this week’s campaign news — but there were other developments, too. Here’s our weekly catch-up on the 2020 election and the Democratic field.

A three-hour tour

Former Vice President Joseph R. Biden Jr. walked into the debate at No. 1 in the polls — and squared off against Nos. 2 through 10 for the first time.

To protect himself from incoming attacks, he brought a trusty shield: the legacy of former President Barack Obama.

As our colleagues Jonathan Martin and Alexander Burns wrote in our debate overview, Mr. Biden “clung tightly to the legacy of the Obama administration” at the debate in Houston on Thursday, “as an array of progressive challengers, led by Senators Elizabeth Warren and Bernie Sanders, brandished more daring policy promises and questioned Mr. Biden’s political strength.” But Mr. Biden also seemed steadier and better prepared than in previous debates.