Who won, who lost and what was too close to call on Tuesday.

Ever since former President Donald J. Trump lost in the state of Georgia during the 2020 presidential election, he has sought revenge against the Republican incumbents there whom he blamed for not helping him overturn the results.

On Tuesday, Mr. Trump lost in Georgia again, with his endorsed candidates losing in their Republican primaries for governor, secretary of state and attorney general.

But those weren’t the only races that voters decided on Tuesday. Here is a rundown of the winners and losers in some of the most important contests in Georgia, Alabama, Arkansas and Texas:

• Georgia’s secretary of state, Brad Raffensperger, won his primary despite Mr. Trump’s best efforts against him.

• The Georgia governor who stood up to Mr. Trump, Brian Kemp, easily defeated a Trump-backed challenger. Mr. Kemp will face Stacey Abrams, the Democratic nominee, whom he narrowly defeated four years ago.

• Chris Carr, Georgia’s attorney general, also defeated his Trump-backed challenger, John Gordon, to win the Republican nomination for that office. Mr. Gordon had embraced Mr. Trump’s election lie and made that a key part of his appeal to voters.

• Herschel Walker, the former football star and a Trump-backed candidate to represent Georgia in the Senate, defeated a crowded field of Republican rivals.

• In Georgia, one House Democrat beat another House Democrat in a primary orchestrated by Republicans.

• Representative Marjorie Taylor Greene won the Republican primary for her House district in Georgia.

• In Texas, a scandal-scarred attorney general defeated a challenger named Bush.

• Sarah Huckabee Sanders, a former White House press secretary under Mr. Trump and the daughter of former Gov. Mike Huckabee of Arkansas, won the Republican nomination for governor of Arkansas.

• Representative Mo Brooks made it into an Alabama Senate runoff after Mr. Trump pulled back his endorsement.

• In Texas, a Democratic House runoff between Representative Henry Cuellar, a Democrat who opposes abortion rights, and his progressive challenger, Jessica Cisneros, an immigration attorney, was too close to call. (Results are being updated in real time here).