In Arizona, one of the nation’s fiercest political battlegrounds, Republicans are looking for candidates who can return their party to statewide power, while Democrats are angling for House seats that could help deliver a majority in November.

Tuesday’s primaries will offer an indication of where voters want their sides to go ahead of the midterm elections.

In races for governor, attorney general, secretary of state and several other positions, the Republican Party’s most Trump-aligned wing is looking to vanquish candidates who argue a more moderate approach is needed to win the general election.

Meantime, Democrats have their eyes on three competitive House districts. The one contested Democratic primary will measure national Democrats’ influence.

Here’s what to know.

Which Republican will challenge Gov. Katie Hobbs?

The Republican primary for governor began as a wide-open affair, with the party still smarting from its 2022 loss to Ms. Hobbs, a Democrat. But in recent months, the party appears to have coalesced around Representative Andy Biggs, a hard-line ally of President Trump.

Mr. Biggs’s most competitive challengers — the developer Karrin Taylor Robson, who dropped out in February, and Representative David Schweikert, who trails far behind in public polls — have argued that he is too extreme to prevail in a general election. Some Republicans worry that nominating Mr. Biggs will lead to a redux of the last cycle, when moderate and independent voters rejected Kari Lake in favor of Ms. Hobbs.

Mr. Biggs has tried hard to convince voters that he is more electable than Ms. Lake was four years ago, despite his far-right record as leader of the House Freedom Caucus. If he wins on Tuesday, expect more moderate positioning from Mr. Biggs and a torrent of messaging from Democrats highlighting his ultraconservative positions, including his efforts to overturn the 2020 election.

Both parties are battling over an open swing seat.

The nonpartisan Cook Political Report rates only one open-seat race in the country as a pure toss up, Arizona’s First Congressional District. Both parties see the stakes as sky-high. Democrats believe control of the House runs through this swingy Scottsdale district, and they see their chances as better than ever since its current occupant, Mr. Schweikert, decided to run for governor.

But the party’s primary has gotten ugly. In a rematch from 2024, Amish Shah, an emergency room physician, is facing Marlene Galán-Woods, a former broadcast journalist and the widow of a prominent Republican critic of Mr. Trump, Grant Woods. The Democratic Congressional Campaign Committee is backing Ms. Galán-Woods, which has infuriated Dr. Shah, who won the nomination last cycle. But his critics point out that Dr. Shah received fewer votes in the district that year than Kamala Harris, and they say Democrats can’t afford another underwhelming performance.

On the Republican side, Jay Feely, a former N.F.L. kicker with Mr. Trump’s endorsement, is trying to fend off Joseph Chaplik, a former state lawmaker running to his right. Before Mr. Feely entered the race, Turning Point USA, the right-wing activist group, had looked to recruit a candidate with some star power, talking with both Danica Patrick, a professional racecar driver, and Jeremy Roenick, a former N.H.L. star, one of the group’s leaders told The New York Times. Both declined to run.

An election denier vies for top elections job.

In the Republican primary for secretary of state, Arizona’s top elections official, the party’s former chairwoman, Gina Swoboda, is running against Alexander Kolodin, a hard-right state lawmaker who has echoed Mr. Trump’s unfounded voting fraud claims about the 2020 presidential election and 2022 governor’s race.

The winner of the primary will face the incumbent, Adrian Fontes, a Democrat, but the race itself is being fought along the new battle lines within Arizona’s Republican Party.

Both Ms. Swoboda and Mr. Kolodin are allies of Mr. Trump. But Ms. Swoboda has said Mr. Kolodin is too conservative and bombastic to beat Mr. Fontes in November, while Mr. Kolodin has accused Ms. Swoboda of being a liberal.

Mr. Kolodin has the backing of Turning Point, which has long feuded with Ms. Swoboda.

Arizona’s first lieutenant governor?

Thanks to a 2022 ballot measure, Arizonans will for the first time elect a lieutenant governor this year. The new office will be the successor to the governor instead of secretary of state.

Candidates for governor choose their lieutenants and run with them on a joint ticket, just like in New York, Florida and many other states. Lieutenant governors won’t be on the ballot Tuesday, but speculation has already begun about whom Ms. Hobbs and the eventual Republican nominee might pick.

Ms. Hobbs’s campaign has floated the possibility of John Giles, a moderate Republican former mayor of Mesa, Ariz., and Jimmy McCain, the son of John McCain, who remains one of the state’s best-known conservatives even years after his death. But both turned her down, according to three people familiar with the outreach who spoke on condition of anonymity to discuss private conversations.

In an interview with The Times, Mr. Biggs declined to say whom he was considering, but he ruled out the possibility of a Democrat.

David W. Chen contributed reporting.