Primary results 2022: California, Iowa, New Mexico, South Dakota and more

Voting has finished in all seven states that held primaries on Tuesday, as California polls closed at 11 p.m. ET. Some high-profile incumbents — including South Dakota Gov. Kristi Noem and Republican Sens. John Thune and Chuck Grassley — have beaten back their primary challengers, and their general election competitors have been determined for November. 

In San Francisco, progressive District Attorney Chesa Boudin was recalled amid worries over crime in the city.  

In many of the races in California, the top two vote getters advance to the November election, regardless of party affiliation, meaning some match-ups could result in two Democrats facing off or two Republicans. 

CBS News projected that Rep. Karen Bass and billionaire real estate developer Rick Caruso will face each other in a runoff in November in the Los Angeles mayor's race. Current Mayor Eric Garcetti is term-limited.

One of the California Republicans facing a primary challenge is Rep. David Valadao, one of the 10 House Republicans who voted to impeach former President Donald Trump. Two Republicans are challenging Valadao in the primary, former city Councilman Chris Mathys and Education Board Trustee Adam Medeiros, but Trump has not endorsed either of them.

CBS News projected Democratic state Assemblyman Rudy Salas will advance to the general election in California's 22nd Congressional District. Democrats are hoping to flip back a seat that was held by a Democrat until 2020.

Democratic Reps. Katie Porter, Josh Harder and Mike Levin are on the target list for national Republicans and are waiting to see who their challenger this November will be. Of the three, Levin may face the toughest race, since his district leans Democratic by only two points, according to data from Dave's Redistricting App. 

CBS News projected Gov. Gavin Newsom will advance to the general election. Sen. Alex Padilla, who was appointed to finish out Vice President Kamala Harris' term, also advanced to the general election in both the regular and special election for U.S. Senate.

Meanwhile in South Dakota, Republican Gov. Kristi Noem, won the Republican nomination for governor after facing a primary challenge from the right. Noem, one of the Republican party's rising stars and possible presidential contender, focused her victory speech on President Joe Biden. She will face Democrat Jamie Smith in November, who ran unopposed on Tuesday. 

Incumbent Sen. John Thune, who is seeking his fourth term, also defeated his primary challengers.

In Iowa, Sen. Chuck Grassley, who is 88, has served in the Senate since 1981, survived his primary challenge from Iowa state Senator Jim Carlin.

Grassley will face Michael Franken, who defeated former U.S. Rep. Abby Finkenauer. She was elected to Congress in 2018, but lost her bid for reelection in 2020. Finkenauer had to fight to get on the ballot after a judge initially ruled that she did not have enough signatures to qualify for the primary ballot. The Iowa Supreme Court reversed that decision several days later.

Franken helped close the gap with Finkenauer, who entered the race as the perceived frontrunner, by outspending her on advertising. He often pitched his military service as helping him appeal to independents and some more moderate Republicans.

"We're going to work very hard. The central premise of this campaign is leadership, which is often overlooked and underestimated. This will propel us," Franken said at a victory party Tuesday night. "It's our time to lead our nation into a better tomorrow."

Republicans have set their sights on Democratic New Mexico Gov. Michelle Lujan Grisham. Television meteorologist Mark Ronchetti won the Republican primary over several challengers to take on Lujan Grisham in November. Lujan Grisham ran  unopposed for the Democratic nomination.

As the House select committee investigating the Jan. 6 attack on the U.S. Capitol prepares for public hearings this month, Democratic select committee Chair Rep. Bennie Thompson won his primary, according to the Associated Press. 

Primaries were also held in New Jersey. Democratic Rep. Tom Malinowski, whose district was redrawn to be more Republican-friendly and won in 2020 by just 1 point, won his primary. Tom Kean Jr. won the Republican primary in New Jersey's 7th District and will face Malinowski, the same matchup as 2020.

In New Jersey's 2nd Congressional District, Trump-endorsed Rep. Jeff Van Drew, who switched parties in 2019 to vote against Trump's impeachment, won his primary. In the 8th District, Robert Menendez Jr., the son of long Sen. Robert Menendez, won the Democratic primary.