Representative Ilhan Omar hopes to continue a string of victories by progressive candidates nationwide, but she faces a well-financed challenge from Antone Melton-Meaux, a lawyer.

A win by Marjorie Taylor Greene would be a headache for G.O.P. leaders since she supports QAnon, a fringe group pushing a pro-Trump conspiracy theory. Her opponent, John Cowan, is no less conservative, but does not believe in a “deep state” of child-molesting Satanist traitors.

Thomas Gilmer was arrested Monday night in connection with a “possible domestic assault,” the police said. He ended his campaign but could still win a spot on the November ballot.

Republicans are fielding a candidate to take on Representative Collin Peterson, a conservative Democrat in a district that voted for President Trump by a 30-point margin.

Republicans would like to unseat Representative Ron Kind in this Democratic-leaning district. Derrick Van Orden, a former Navy Seal, is well-funded, has former Gov. Scott Walker’s endorsement and recently got publicity for saving a woman from choking in a local restaurant.