Read updates below from states that held primaries Tuesday night:
Vermont primary results
Hallquist becomes first transgender gubernatorial nominee
Incumbent Gov. Phil Scott won the Republican nomination for governor. Christine Hallquist won the Democratic nomination for governor, making her the first transgender gubernatorial candidate in the country.
"Vermonters are going to elect me for what I'm going to do for Vermont," Hallquist said. "Vermont has always been a leader in civil rights. We have some of the best transgender protection laws in the country. It's a state that's really welcomed me with open arms."
Scott's popularity in the state has dropped since he signed gun control laws in April. A Morning Consult poll from July found that Scott had an approval rating of 47 percent, a 38 point drop in approval since May 2016. Businessman Keith Stern challenged Scott from the right.
Through a loophole in Vermont's laws, 14-year-old Ethan Sonneborn ran for the office as a Democrat. Vermont's Constitution doesn't have an age requirement, it just requires candidates to have lived in the state for four years.
"I think Vermonters should take me seriously because I have practical progressive ideas, and I happen to be 14, not the other way around," the 14-year-old said in a recent gubernatorial forum. "I think that my message and my platform transcend age."
Sonneborn spoke with CBS News reporter Ed O'Keefe about his candidacy.
Sen. Bernie Sanders has easily won Vermont's Democratic primary, according to the Associated Press. However, Sanders is expected to turn down the nomination, as he has in the past, and continue serving as an independent.
Connecticut primary results
Lamont wins Democratic nod for governor
Businessman Ned Lamont has won the Democratic primary for governor, the Associated Press reports. Matthew Corey, a Navy veteran and businessman, won the Republican primary.
On the Democratic ballot, voters chose between Mayor Joe Ganim and Lamont. Ganim was Mayor of Bridgeport from 1991 to 2003, when he resigned after being convicted on corruption charges. He then launched a remarkable political comeback after serving seven years of a nine-year prison sentence, becoming Bridgeport's mayor once again in 2015.
Bob Stefanowski won the Republican nomination for governor with the plurality of the vote in a five-way race.
Other races to watch include the Democratic and Republican primaries for the opening seat in Connecticut's 5th Congressional District. Rep. Elizabeth Esty, a Democrat, is not seeking a fourth term.
Jahana Hayes won the Democratic nomination for the 5th Congressional District over establishment candidate Mary Glassman, who had been endorsed by the U.S. Chamber of Commerce. Manny Santos won the Republican nomination. Hayes' win now paves the way for her to become the state's first black woman to serve in Congress should she win in November.
Wisconsin primary results
Walker wins primary as he seeks his third term
Democrats have so far been unable to unseat Republican Gov. Scott Walker, but they hope to do so come November. Walker prevailed in a recall election in 2012 and then again in 2014.
Walker easily won his primary race against Robert Meyer.
The Democratic field in the race for governor was a crowded one, with eight contenders. Tony Evers, the state's superintendent of public instruction, won the nomination.
Meanwhile, Democratic Sen. Tammy Baldwin will face off in November against GOP nominee Leah Vukmir.
Paul Ryan's replacement
University of Wisconsin regent Bryan Steil, who was endorsed by House Speaker Paul Ryan, won a five-way Republican primary to replace Ryan, who is not running for re-election. Paul Nehlen, the controversial candidate who unsuccessfully ran against Ryan in 2016, unsuccessfully ran. for the seat.
On the Democratic side, Randy Bryce won the nomination, despite his history of arrests, including one for driving while intoxicated in 1998.
Minnesota primary results
Tina Smith fends off primary challenge
The departure of former Sen. Al Franken means both of the state's Senate seats are up for grabs this fall. Franken left office in January amid #MeToo allegations.
Former George W. Bush ethics lawyer Richard Painter lost to current Sen. Tina Smith, who was appointed to take Franken's seat, in the Democratic primary. Sen. Amy Klobuchar, a Democrat, is also running for the Democratic nomination to keep her seat. She will be facing Republican Jim Newberger.
In the gubernatorial race, Jeff Johnson won the Republican nomination for governor. Former Republican Gov. Tim Pawlenty, a late entrant to the race, unsuccessfully sought his party's nomination. Tim Walz won the Democratic nomination for governor.
Ellison wins primary despite controversy
Rep. Keith Ellison easily won the Democratic nomination for attorney general. Ellison was accused of abuse by a former girlfriend. Ellison has denied the allegation. Ellison is currently the deputy chair of the Democratic National Committee.
State Rep. Ilhan Omar, the country's first Somali-American lawmaker, won the Democratic primary in the race to replace Ellison. In Minnesota's 8th Congressional District, Trump-endorsed candidate Pete Stauber won the Republican primary.
Kansas Gov. Jeff Colyer concedes to Kris Kobach in primary
Kobach maintained a slim lead over Colyer
Kansas Gov. Jeff Colyer conceded to Kris Kobach in the Republican primary on Tuesday night. Kobach, the current secretary of state, held a slim lead over Colyer on election night Aug. 7. Provisional ballots counted after election night did not find enough votes for Colyer to overcome a deficit of 110 votes at the time of poll closing, out of more than 311,000 votes initially counted.