The presidential primary contests may be over, but there are plenty of consequential downballot elections still to come.

Voters across the country will vote on next Tuesday night on combatting homelessness in Illinois, choosing candidates who could determine which party controls Congress next year and replacing ousted Speaker of the House Kevin McCarthy.

Here’s a look at some races to watch.

Key contests in Ohio

Ohio used to be the nation’s premier swing state but has lurched to the right since former President Donald Trump’s election in 2016. Yet Democratic Sen. Sherrod Brown has proven tough for Republicans to dislodge. They get another shot this year and on Tuesday will pick one of three candidates with markedly different styles to face the state’s senior senator.

Trump has endorsed former car dealer and blockchain entrepreneur Bernie Moreno, who is running firmly in the Trump lane as a political outsider eager to shake things up. He faces another businessman, Matt Dolan, whose family owns the Cleveland Guardians and he has tried to consolidate the party’s moderate middle in the race, not even seeking Trump’s endorsement. Rounding out the trio is Secretary of State Frank LaRose, an Army veteran who unsuccessfully sought Trump’s nod.

All three support national restrictions on abortion, limiting discussion of sexuality and transgender issues in schools, and cracking down on illegal immigration. But Moreno is the most confrontational of the trio and some Republicans worry he could provide a bigger target for Democratic attacks. Moreno’s supporters argue he’s more likely to win over the state’s populist voters.

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AP Decision Notes: What to expect in the Tuesday presidential and state primaries

Democrats hold a 51-49 majority in the U.S. Senate and Republicans have several chances this fall to pull ahead. Ohio is one of three states, along with Montana and West Virginia, that supported Trump in 2020 but have a Democratic-held Senate seat up in 2024.

Ohio may also be the Republican gateway to retaining control of the even more narrowly divided House of Representatives. The state’s GOP-controlled legislature redrew House seats in 2021 to transform the northwestern district held by Democratic Rep. Marcy Kaptur. But Republicans lost the race to oust her in 2022 after nominating J.R. Majewski, a firebrand pro-Trump political novice who misrepresented his military service.

Majewski was the leading contender in this year’s Republican primary, too, leading party leaders to fear he would lose another winnable seat. But earlier this month he abruptly announced he was leaving the race. The decision came just days after Majewski insisted, amid pressure over his military service record and remarks he’d made on a podcast denigrating Special Olympics athletes, that he was staying in.

Majewski’s name remains on the ballot, but Republicans hope that one of two other candidates considered more viable —- State Rep. Derek Merrin and former State Rep. Craig Riedel — ends up facing Kaptur in November.

Chicago’s homeless tax

Like many big cities, Chicago has been wrestling with homelessness. And the city’s progressive leaders have zeroed in on high-priced real estate as a way to deal with the problem.

Voters will decide on a one-time tax on real estate valued at more than $1 million that advocates say would generate $100 million for homeless services like mental health and job training.

Led by Mayor Brandon Johnson, the city’s liberals have backed the initiative, which would lower property taxes for parcels valued under $1 million. But real estate groups oppose the measure, saying it unfairly targets commercial properties at a time when the city’s downtown office buildings are struggling to recover from the pandemic.

Trump’s downstate clout

Also in Illinois but political light-years from deep blue Chicago, Republican Rep. Mike Bost faces a primary challenge from Darren Bailey, a farmer who founded a Christian school in a downstate district.

Bailey was the GOP nominee for governor in 2022. Democrats boosted him in the Republican primary because he was seen as an easier opponent for Democratic Gov. J.B. Pritzker, who beat him by 13 percentage points. His brand of Christian conservatism plays better in the rural 12th Congressional District.

Bailey has visited Trump’s Florida compound and declares himself the heir to the former president’s populist movement. But Trump has actually endorsed Bost in the primary. That makes this race the latest test of whether Trump can get voters to pay attention to his favored candidates, or just the candidate with the strongest Trump vibes.

A McCarthy replacement

Tuesday is the special election to choose someone to finish out former House Speaker Kevin McCarthy’s term. McCarthy was ousted from his speakership last fall and resigned his seat afterward. The contenders in California’s Central Valley resemble those in downstate Illinois — a Republican from the more mainstream wing of the party with Trump’s endorsement trying to hold off a challenger running as an outsider.

In California’s 20th Congressional District, that’s one of McCarthy’s former aides and his chosen successor, Assemblyman Vince Fong, with the Trump endorsement. He’s fending off a challenge from Tulare County Sheriff Mike Boudreaux, who’s run as a law-and-order populist.

Earlier this month, Fong and Boudreaux scored the first two positions in California’s top-two primary system, advancing to a November faceoff for whoever will take the seat in early January. Tuesday’s election is just to fill the McCarthy seat until the beginning of next year, but it’ll be noteworthy whether the same dynamic holds.

Final presidential signs

The presidential primary season largely ended this week with Biden and Trump both winning enough delegates to become their parties’ presumptive nominees. There’s been little suspense with both men dominating, so political junkies have instead scoured the lopsided wins to find signs of weakness for November.

That can continue even though the primaries are now more ceremonial.

Last Tuesday, former U.N. Ambassador Nikki Haley won 13% of the Georgia Republican primary vote despite having suspended her campaign the prior week. That reflects how Georgia Republicans were able to cast their ballots by mail starting in February, before Haley stopped campaigning. But it also highlights concerns about Trump among some of his party’s suburban voters that have dogged him since he entered politics.

It’s worth watching Haley’s numbers in Tuesday’s states to see if there’s still a protest vote in the GOP primary or whether Georgia was just a mail ballot echo.

Likewise, Biden has been dogged by protest votes against his handling of the Gaza war, with large shares of Democratic primary voters marking their ballots as uncommitted in Michigan, Minnesota and elsewhere. It’s also worth watching to see if any trace of a protest vote remains on the Democratic side in states like Kansas, which offers the option of choosing “none of the names shown.”