[Follow results of the N.Y.C. mayoral race and other New York elections.]

A lot of the political world’s consideration on Tuesday might be targeted on Virginia, the place former Gov. Terry McAuliffe, a Democrat, is making an attempt to return to his previous workplace in a run towards Glenn Youngkin, a rich Republican enterprise government.

Polls present the race is a useless warmth. And the themes of the competition — with Mr. McAuliffe making an attempt relentlessly to tie Mr. Youngkin to former President Donald J. Trump, and Mr. Youngkin specializing in how racial inequality is taught in colleges, amongst different cultural issues — have solely amplified the election’s potential as a nationwide bellwether. The outcomes might be carefully studied by each events for clues about what to expect in the 2022 midterms.

Whereas the Virginia race is Tuesday’s marquee matchup, there are different notable elections going down. Voters in lots of main American cities will select their subsequent mayor, and a few will weigh in on hotly contested poll measures, together with on the difficulty of policing. There’s one other governor’s race in New Jersey, too. Here’s what to look at in a number of the key contests that may present probably the most detailed and textured look but at the place voters stand greater than 9 months into the Biden administration.

Democrats have received Virginia in each presidential contest since 2008. Final 12 months, it wasn’t significantly shut. Mr. Biden received by 10 share factors.

However Virginia additionally has a historical past of bucking the occasion of a brand new president — the state swung to the G.O.P. in 2009, throughout former President Barack Obama’s first 12 months in workplace — and Republicans hope Mr. Youngkin has discovered a method for fulfillment within the post-Trump period.

To prevail, Mr. Youngkin wants to chop into the margins in suburban Northern Virginia, the place voters have made the state more and more Democratic, whereas additionally turning out a Republican base that is still motivated by Mr. Trump.

His playbook has targeted closely on training, attacking Mr. McAuliffe for a debate comment that folks shouldn’t be directing what colleges educate and capitalizing on a broader conservative motion towards colleges instructing about systemic racism. The end result: Education has been the top issue within the race, in keeping with an October Washington Post poll, giving Republicans the sting on a subject that has historically favored Democrats.

Mr. McAuliffe has aggressively linked Mr. Youngkin to Mr. Trump, who endorsed the Republican however by no means traveled to Virginia to marketing campaign for him. If Mr. Youngkin loses, it would showcase the G.O.P.’s ongoing problem in being related to Mr. Trump, even with out Mr. Trump on the poll. But when Mr. McAuliffe loses, it would intensify stress on Democrats to develop a brand new, proactive message.

Management of the Virginia Home of Delegates can be up for grabs. For now, Democrats have an fringe of 55-45 seats that they constructed throughout the Trump years.

Within the New Jersey governor’s race, the Democratic incumbent, Philip D. Murphy, is up for re-election. Polls have proven Mr. Murphy forward, however Mr. Biden’s weakening job approval ranking within the solidly Democratic state — which stood at 43 percent in a current Monmouth ballot — is a explanation for concern. The outcomes might be watched for proof of how a lot of the erosion in Mr. Biden’s assist has seeped down-ballot.

It’s not the largest metropolis with a mayor’s race on Tuesday, however the City Hall battle in Buffalo, N.Y., will be the most fascinating.

India Walton, who can be the primary socialist to steer a serious American metropolis in a long time, defeated the incumbent Democratic mayor, Byron Brown, within the June main. However Mr. Brown is now operating a write-in marketing campaign.

Ms. Walton has received the backing of progressives, comparable to Consultant Alexandria Ocasio-Cortez, and a few occasion leaders, like Senator Chuck Schumer, however different distinguished Democrats have stayed impartial, most notably Gov. Kathy Hochul, a lifelong resident of the Buffalo area.

Policing has been a serious concern. Although Ms. Walton has distanced herself from wanting to cut back police funding, Mr. Brown attacked her on the difficulty in a television ad.

In Boston, the runoff places two Metropolis Council members, Michelle Wu and Annissa Essaibi George, towards one another, with Ms. Wu operating because the progressive. Ms. Wu, who’s backed by Senator Elizabeth Warren of Massachusetts, completed in first place within the main.

In New York Metropolis, Eric Adams, the borough president of Brooklyn and a Democrat, is predicted to win the mayor’s race and has already common himself as a nationwide determine. “I’m the face of the brand new Democratic Occasion,” Mr. Adams declared after his June main win.

In Miami, Mayor Francis Suarez, a uncommon big-city Republican mayor, is closely favored to win re-election and is lined as much as change into the president of the U.S. Convention of Mayors, giving him a nationwide platform.

And in Atlanta, a crowded subject of 14 candidates, together with the Metropolis Council president, Felicia Moore, is predicted to result in a runoff as former Mayor Kasim Reed makes an attempt to make a comeback.

One recurring theme in municipal races is policing, as communities grapple with the “defund the police” slogan that swept the nation following the police killing of George Floyd final 12 months. The talk is raging contained in the Democratic Occasion over how a lot to overtake regulation enforcement — and over the right way to speak about such an overhaul.

Maybe nowhere is the difficulty extra central than in Minneapolis, the town the place Mr. Floyd was killed, sparking civil unrest throughout the nation. Voters there’ll determine on a measure to replace the troubled Minneapolis Police Department with a brand new Division of Public Security.

Mayor Jacob Frey, who’s up for re-election, has opposed that measure and pushed for a extra incremental strategy. His challengers, amongst them Sheila Nezhad, need a extra aggressive strategy.

Policing is a key concern not solely within the Buffalo mayor’s race, but in addition in mayoral contests in Seattle, Atlanta and in Cleveland, the place an modification that may overhaul how the town’s police division operates is on the poll as effectively.

The mayor’s race in Cleveland places Justin Bibb, a 34-year-old political newcomer, towards Kevin Kelley, the Metropolis Council president. Mr. Bibb supports the police amendment and Mr. Kelley opposes it.

There are two particular elections for Home races in Ohio, with Shontel Brown, a Democratic Cuyahoga County Council member, anticipated to win a closely Democratic seat in Cleveland. Mike Carey, a longtime Republican coal lobbyist, is favored in a district that sprawls throughout a dozen counties.

Mr. Carey faces Allison Russo, a Democrat endorsed by Mr. Biden. Mr. Carey’s margin in a seat that Mr. Trump carried by greater than 14 factors final 12 months might be one other useful indicator of the political setting.

In Florida, a main is being held for the seat of Consultant Alcee Hastings, who died earlier this 12 months. The winner might be favored in a January particular election.

The one statewide races taking place in Pennsylvania on Tuesday are for the courts. Essentially the most carefully watched contest is for the State Supreme Court docket, which options two appeals court docket judges, the Republican Kevin Brobson and the Democrat Maria McLaughlin. Democrats at the moment maintain a 5-2 majority on the court docket and the seat being vacated was held by a Republican, so the end result is not going to swing management.

However tens of millions of {dollars} in promoting are pouring into the state, an indication not simply of the rising politicization of judicial contests, but in addition of the state’s function as a prime presidential battleground.

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