5 States Are Voting on Tuesday. Here’s What to Watch.

A look at the most important primaries in Kansas, Michigan, Missouri and Washington, and a special election in Ohio.

Tuesday is another busy voting day, with Kansas, Michigan, Missouri and Washington holding primaries and one Ohio district holding a special House election. We’ll have live results beginning Tuesday evening.

Here’s a look at the most important races.

Troy Balderson, a Republican, spoke at a rally with president Trump in Lewis Center, Ohio, on Saturday.CreditAl Drago for The New York Times
Danny O’Connor, a Democrat, knocked on doors in New Albany, Ohio, last month.CreditMaddie McGarvey for The New York Times

Voters in Ohio’s 12th District will choose a replacement for Representative Pat Tiberi, a Republican who resigned to work for a business group. The candidates are Troy Balderson, a Republican endorsed last week by Mr. Trump, and Danny O’Connor, a Democrat.

The race is expected to be close, and both national parties are spending heavily. But whoever loses will get a rematch in the regularly scheduled election in just three months. Read more about what’s a stake here.

Kansas Secretary of State Kris Kobach is a firebrand on immigration as well as voting laws.CreditCharlie Riedel/Associated Press

At the top of the ballot here is the race for governor, a job held by Jeff Colyer since the former governor, Sam Brownback, accepted an ambassadorship under President Trump.

Gov. Colyer is running against Secretary of State Kris Kobach, the face of Mr. Trump’s voter fraud commission, in the Republican primary. In a dynamic that has become very familiar this year, each man wants to be known as the most loyal and effective ally of the president. Mr. Kobach, a firebrand on immigration as well as voting laws, resembles the president in tone and style, leaving Mr. Colyer to argue that he is a pragmatist who will more effectively accomplish Trumpian policy goals. Mr. Trump endorsed Mr. Kobach on Monday.

Also running are three Democrats: Carl Brewer, a former mayor of Wichita; Laura Kelly, a state senator; and Joshua Svaty, a farmer and former state agriculture secretary. Some Democrats think that if Mr. Kobach wins the Republican nomination, it could give them an opening among voters who see him as too extreme. Read more about that possibility here.

Finally, voters will be choosing their candidates in two Republican-held House districts that Democrats hope to flip in November. Seven Republicans are on the ballot in the Second District, where Representative Lynn Jenkins is retiring; the winner will face Paul Davis, a Democrat who won the district during his unsuccessful bid for governor in 2014. And in the Third District, which includes Democratic-leaning Kansas City and Overland Park, six Democrats are vying to challenge Representative Kevin Yoder.

Read more about the Kansas primaries

Four Republicans and three Democrats are running for governor here, a wide-open race since Gov. Rick Snyder has reached his term limit. On the Republican side, the top contenders appear to be Attorney General Bill Schuette and Lt. Gov. Brian Calley. On the Democratic side, the candidates are the former State Senator Gretchen Whitmer; Shri Thanedar, a businessman; and Abdul El-Sayed, a progressive former director of the Detroit Health Department.

Meanwhile, two businessmen are running in a Republican primary to challenge Senator Debbie Stabenow, a three-term Democratic incumbent who is running for re-election. This is yet another race in which the candidates are jockeying for the Trump vote, and Mr. Trump weighed in late last month, endorsing John James over Sandy Pensler. A poll conducted shortly before the endorsement showed an extremely close race, but Mr. Trump’s support could give Mr. James the edge.

Read more about the primaries in Michigan.

Five House races in Michigan are also expected to be competitive in November, especially the Republican-held Eighth and 11th Districts. In the Eighth District, two Democrats — Elissa Slotkin and Chris Smith — are vying to challenge Representative Mike Bishop. And in the 11th District, where Representative David Trott is retiring, there are crowded primary fields on both sides.

Keep an eye, too, on the 13th District, where Representative John Conyers Jr. resigned last year because of sexual harassment allegations. It’s a safe Democratic seat, but the primary is hard-fought. Read more about the candidates in that race here.

Mr. Trump has fundraised and campaigned for Josh Hawley, a Republican candidate for Senate.CreditDoug Mills/The New York Times
Senator Claire McCaskill could run a close race for re-election in November.CreditAl Drago for The New York Times

Senator Claire McCaskill is believed to be one of the most vulnerable Democrats in the Senate because of her low approval rating and Mr. Trump’s victory in Missouri by nearly 20 percentage points. Six years ago, she managed to win re-election largely because of the deep unpopularity of her Republican opponent, Todd Akin, who drew national ridicule and condemnation for claiming that women did not get pregnant in cases of “legitimate rape.” This time, Republicans are hoping to nominate a stronger challenger.

The front-runner is Josh Hawley, Missouri’s conservative attorney general, for whom Mr. Trump has raised funds and campaigned; his long-shot opponent is Austin Petersen, a libertarian. Polls show an extremely close race between Mr. Hawley and Ms. McCaskill.

In the First Congressional District, Cori Bush is running against an incumbent Democrat, William Lacy Clay, in a test of whether the progressive playbook pioneered by Alexandria Ocasio-Cortez in New York can work in the heartland. Read more about that race here.

Voters will also weigh in on a ballot measure that will determine whether Missouri becomes a right-to-work state, meaning that workers would no longer have to join a union or pay fees if their workplace is unionized. Republicans passed right-to-work legislation in 2017, but labor groups collected enough signatures to prevent the measure from taking effect pending a statewide ballot.

Two of Washington’s 10 congressional districts have competitive races on Tuesday. The primaries will be “top two,” meaning that — as in California — the top two finishers will move on to the general election, regardless of party.

In the Eighth District, four main candidates are running to replace Representative David Reichert, a retiring Republican whose seat is considered a tossup this year. Former State Senator Dino Rossi, a Republican, is expected to finish comfortably in the top two in the primary. The big question is which Democrat will make it along with him: Shannon Hader, a former official at the Centers for Disease Control and Prevention; Jason Rittereiser, a lawyer; or Kim Schrier, a pediatrician.

In the solidly Democratic Ninth District, Representative Adam Smith, a longtime congressman with a top position on the House Armed Services Committee, is facing a primary challenge from Sarah Smith, a democratic socialist. On the surface, this looks a lot like New York’s 14th District, where another democratic socialist, Ms. Ocasio-Cortez, beat Joseph Crowley, a longtime congressman with a powerful leadership position. Ms. Smith has encouraged the comparison, while Mr. Smith has emphasized the differences between the two races — including the fact that Ms. Ocasio-Cortez was born and raised in her district, while Ms. Smith lives just outside this one.

Noam Scheiber contributed reporting.

Maggie Astor is a political reporter based in New York. Previously, she was a general assignment reporter and a copy editor for The Times and a reporter for The Record in New Jersey. @MaggieAstor