Patricia Mazzei

By Dr. Annie Andrews, the Democratic nominee for Senate in South Carolina, spent more than a year running to unseat Sen.

Gov. Henry McMaster of South Carolina said Monday that he would appoint Sen. Lindsey Graham's sister, Darline Graham Nordone, to finish his Senate term, after Graham's death Saturday.

Representative Andy Ogles received President Trump’s endorsement, but his challenger, Charlie Hatcher, a former state agriculture commissioner, has the backing of Gov. Bill Lee.

Two Republican lawmakers have endorsed a primary opponent of Representative Cory Mills, who has been accused of assault and is under investigation by the House Ethics Committee.

The left and the middle continue to battle in Democratic primaries for governor in Wisconsin and Senate in Minnesota. In South Carolina, all eyes are on Darline Graham.

A democratic socialist is seeking the nomination for governor of Wisconsin, and the late Senator Lindsey Graham’s sister is competing in a primary for his seat. Four other states are also holding races.

The two-term Republican congressman, who once interned in the office of Senator Lindsey Graham, has campaigned in part on his youth.

The longtime lawmaker, a member of an ultraconservative group of House members, came in third place in the Republican primary for governor this year.

Senator Darline Graham will face Representative Ralph Norman in a runoff for the G.O.P. nomination for the seat held by her late brother. Polls have closed in five other states, including Minnesota and Wisconsin, where a democratic socialist is seeking the nomination for governor.

COLUMBIA, S.C. — An agonizingly close race in the Democratic primary for governor of Wisconsin ended with an upset win for moderate David Crowley early Wednesday, the latest turn in a rancorous battle between the party's ascendant left and its old guard that has defined primary season this year.