Votes are being tallied in Alabama, California, Iowa, Mississippi, Montana, New Jersey, New Mexico and South Dakota.
Some of the highlights:
WOMEN IN THE GOVERNOR'S OFFICE
In a record-setting year for female candidates across the country, Michelle Lujan Grisham won the Democratic nomination for New Mexico governor. She would be the first Latina Democratic governor in U.S. history.
Lujan Grisham, a congresswoman, is trying to succeed the nation's first Latina Republican governor, Susana Martinez. Republicans also nominated a member of Congress, Rep. Steve Pearce, to run for the job.
Another congresswoman, South Dakota's Kristi Noem, won her state's Republican gubernatorial primary. She would become the first female governor in South Dakota history.
Voters in Alabama and Iowa had opportunities to set up all-female matchups for governor in November.
Alabama's Republican Gov. Kay Ivey avoided a runoff despite several primary challengers. But Democrats chose Tuscaloosa Mayor Walt Maddox over Sue Bell Cobb, a former state Supreme Court chief justice.
In Iowa, labor leader Cathy Glasson couldn't pull off an upset against businessman Fred Hubbell for the Democratic nomination, so Hubbell will take on Republican Gov. Kim Reynolds, who had no party opposition.
Both Reynolds and Ivey are vying for their first full terms after succeeding men who resigned. Reynolds is Iowa's first female governor. Ivey is the second woman to helm Alabama government, but the first in five decades.
Democratic Sen. Bob Menendez of New Jersey got a primary challenge after a hung jury spared him a conviction in a federal bribery trial. But Menendez held on, to the delight of Republicans who want to use his troubles to tar every Democrat in the state. Menendez will face Republican Bob Hugin, a pharmaceutical executive, in the fall.
Democratic Sen. Jon Tester of Montana is waiting to find out who his Republican challenger will be in November. The most likely nominees are State Auditor Matt Rosendale and retired judge Russ Fagg. Rosendale has GOP establishment support, but that may not be a plus for Montana Republican voters.
Mississippi's Republican Sen. Roger Wicker coasted to his party's nomination Tuesday, and he'll be a big favorite in November. Democrats will have a runoff between Howard Sherman and David Baria.
California Sen. Dianne Feinstein advanced to the November ballot by leading a gaggle of candidates in her state's so-called jungle primary, which puts all candidates on the same ballot, with the top two vote-getters moving forward. Feinstein will be the heavy favorite in the second round, where she's likely to face another Democrat, state Senate leader Kevin de Leon, who's running to Feinstein's left.
BATTLE FOR HOUSE CONTROL
Democrats are looking to New Jersey and California as key states in their efforts to gain at least 23 more House seats and become the majority when Congress convenes next year.
A former Obama administration aide, Andy Kim, will take on New Jersey GOP Rep. Tom McArthur. It's one of five New Jersey GOP House seats targeted by national Democrats.
Among the others, Democrat Tom Malinowski, an appointee in the Obama State Department, won the nomination to take on vulnerable Republican Rep. Leonard Lance.
Navy veteran and former federal prosecutor Mikie Sherrill claimed the Democratic nomination in a district left open by the retirement of Republican Rodney Frelinghuysen. The GOP race was still too close to call a few hours after polls closed.
In southern Jersey, a conservative Democratic state senator, Jeff Van Drew, dispatched more liberal competitors in a Republican-leaning district now held by Frank LoBiondo, who is retiring. The GOP race was still too close to call.
California's outcomes probably won't be decided Tuesday because the state allows mail-in ballots to be postmarked through primary day. But the focus is on seven House districts where President Donald Trump trailed Hillary Clinton in 2016.
In three of those districts, all in southern California, Democrats faced the possibility of being shut out of the top two spots because they have so many candidates.
In Alabama, a Republican incumbent who criticized Trump as a candidate in 2016 is headed for a runoff. Rep. Martha Roby led her GOP competitors but fell shy of a required majority. She'll face former Rep. Bobby Bright, whom she defeated in 2010. Bright was then a Democrat.
California Republicans hope to avoid another statewide shutout in the contest for governor.
Democratic Lt. Gov. Gavin Newsom is expected to lead the governor's primary. The second spot probably will go either to former Los Angeles Mayor Antonio Villaraigosa, a Democrat, or Republican business executive John Cox.