Voters in Kentucky are choosing their nominees on Tuesday for governor and other statewide offices. Gov. Matt Bevin, the Republican incumbent, is deeply unpopular, and Democrats see an opening to retake a red-state governorship in the fall.

The polls are open until 6 p.m. local time. Here’s what to watch for when the results start coming in.

Who will challenge Governor Bevin?

Mr. Bevin, a conservative Republican first elected in 2015, has the dubious distinction of being the least popular governor in the country, according to the polling organization Morning Consult. And while Kentucky is reliably red in federal elections, Democrats there have often been successful in state races, which makes them hopeful that they can unseat Mr. Bevin in November.

Whether they succeed will depend in part on whom they nominate. There are four choices: State Representative Rocky Adkins; Andy Beshear, the state attorney general; Adam Edelen, a former state auditor; and Geoff Young, an activist and perennial political candidate.

[Here’s our results page for the Kentucky governor primary.]

Mr. Beshear is the best known, and his father, Steve Beshear, was governor from 2007 to 2015. He has focused his campaign on economic issues, including health care and the state’s pension crisis. The abortion rights group Naral is supporting him, which could be significant given the increased focus on abortion policy in state legislatures. Kentucky, like a number of other states, passed a highly restrictive abortion law this year, known as a “heartbeat bill” — though it has not yet taken effect — and Mr. Bevin has called himself “the most pro-life governor in America.”

But Mr. Edelen has energized liberal Kentuckians and has received some prominent endorsements, including from the state’s largest newspaper, The Courier Journal. Mr. Adkins, who has been focusing on the state’s rural areas, has the support of labor groups and is on the other side of the abortion debate: He voted for the abortion bill, which would ban the procedure after six weeks of pregnancy, and he has supported other restrictions in the past.

Mr. Young has not campaigned much, The Courier Journal reported, and is not expected to win.

Will Bevin survive his own primary?

Mr. Bevin is facing three Republican primary challengers, but despite his low approval ratings, polls show him comfortably ahead of them.

State Representative Robert Goforth, Mr. Bevin’s strongest competitor, is running to his right, though the governor is himself very conservative. Mr. Goforth has criticized Mr. Bevin’s combativeness and penchant for insults, which is a common complaint among voters, too.

The other two Republican candidates, Ike Lawrence and William Woods, are running “limited campaigns,” according to The Lexington Herald-Leader.

What about the other races?

While attention has focused overwhelmingly on the governor’s race, there are several other primary races taking place on Tuesday, including for secretary of state and attorney general.

Secretary of State Alison Lundergan Grimes, a Democrat, cannot run again because of term limits, and four candidates from each party are running to replace her. The Democratic candidates are Jason Belcher, Heather French Henry, Jason Griffith and Geoff Sebesta; the Republican candidates are Michael Adams, Andrew English, Stephen Knipper and Carl Nett.

In the race to replace Mr. Beshear as attorney general, Greg Stumbo — who previously served as attorney general from 2004 to 2008 — is running unopposed for the Democratic nomination. There are two Republican candidates, Daniel Cameron and Wil Schroder.

[Here’s our results page for all of Tuesday’s primaries in Kentucky.]

Follow Maggie Astor on Twitter: @MaggieAstor.

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