Voters cast ballots in Minnesota, Georgia, Connecticut, Wisconsin and Vermont

Primary elections are being held on Tuesday in Minnesota, Georgia, Connecticut, Vermont and Wisconsin.

The big picture: Georgia and Wisconsin both struggled to hold primaries during the coronavirus pandemic, but are doing so again — testing their voting systems ahead of the general election. Rep. Ilhan Omar (D-Minn.) is facing a strong challenger as she fights for her political career. In Georgia, a Republican primary runoff pits a QAnon supporter against a hardline conservative.

Races to watch:

In Minnesota, Omar is facing off against Antone Melton-Meaux, a well-financed lawyer. If Omar loses, center-left Democrats can claim a rare win. They have consistently lost to more progressive challengers across the country, The New York Times writes.

• The race between Omar and Melton-Meaux again matches a progressive against a more moderate challenger — a contest that's played out in other states to the benefit of progressives.
• Omar is the last member of "The Squad" to go through a primary challenge. Reps. Alexandria Ocasio-Cortez (D-N.Y.), Ayanna Pressley (D-Mass.) and Rashida Tlaib (R-Mich.) all sailed to victory.
• Both Melton-Meaux and Omar have labeled themselves as progressive, but the key divider is their stance on Israel. Omar has been outspoken against Israel, while Melton-Meaux has expressed his support.
• Omar won House Speaker Nancy Pelosi's endorsement last month, the Times notes.

Of note: Omar has raised $4.2 million, and Melton-Meaux has just over $4.1 million in his war chest, according to the Federal Election Commission.

In Georgia, Marjorie Taylor Greene and John Cowan will meet again, this time in a runoff to represent the state's 14th Congressional District. Both are hardline conservatives and supporters of President Trump in a district that is solidly red. The winner of Tuesday's contest is expected to win the seat in November.

• Greene has built a platform for herself as a gun-rights activist and QAnon supporter, a fringe group that pushes a pro-Trump conspiracy theory. More than a dozen candidates for Congress have now expressed support for QAnon.
• House Republicans have spoken out against Greene after videos of her making racist statements surfaced on Facebook. However, the party has done little to stop her success. House Minority Whip Steve Scalise (R-La.) is the only House GOP leader to help Cowan, Politico reports.

The state of play: Greene is favored to win the runoff, per the Times. She won 40% of the vote on June 16 to Cowan's 21%.

Republican Rep. Doug Collins has opted to run for Senate, leaving his seat open. State Rep. Matt Gurtler is facing off against Navy veteran Andrew Clyde in Georgia's 9th Congressional District, NPR reports.

• Nearly 60% of the state's counties are holding primary elections, but turnout still isn't expected to be high.

Wisconsin's election system will be the real star of the night. It was the first state to hold a large, statewide election after a coronavirus surge in April, the Times notes.

The state of play: About 95% of voting sites will be open in Milwaukee. The state has also called on the National Guard to be onsite to help in the case of poll worker shortages.

• Republican Rep. Jim Sensenbrenner is retiring from his seat in Wisconsin's 5th Congressional District. State Senate Majority Leader Scott Fitzgerald has Sensenbrenner's endorsement and faces off against Cliff DeTemple, a longtime military reservist, NPR reports.

Connecticut is the last state to hold presidential primaries, days before Republican and Democratic parties prepare for their conventions.

• Thomas Gilmer dropped out of his Republican primary race after he was arrested Monday night. He has been charged with strangulation and unlawful restraint in connection with a "possible domestic assault," per the Times.
• Gilmer was to face off against Justin Anderson, a lieutenant colonel in the National Guard. The primary winner will face Democratic incumbent Rep. Joe Courtney.

In Vermont, six-term incumbent Rep. Peter Welch (D) is running against Ralph Corbo for the Democratic nomination for the state's lone at-large House seat, The Burlington Free Press reports. The state will also be voting in primaries for governor and lieutenant governor.