What to watch in Tuesday’s elections: Virginia, mayoral races and policing measures.

Most of the governmental world’s attraction connected Tuesday volition beryllium focused connected Virginia, wherever erstwhile Gov. Terry McAuliffe, a Democrat, is trying to instrumentality to his aged bureau against Glenn Youngkin, a affluent Republican concern executive. Polls amusement the contention is simply a dormant heat. And the themes of the contention — with Mr. McAuliffe trying relentlessly to tie Mr. Youngkin to erstwhile President Donald J. Trump, and Mr. Youngkin focusing connected however radical inequality is taught successful schools, among different cultural issues — person lone amplified the election’s imaginable arsenic a nationalist bellwether. The results volition beryllium intimately studied by some parties for clues astir what to expect successful the 2022 midterms.

While the Virginia contention is Tuesday’s marquee matchup, determination are different notable elections taking place. Voters successful galore large American cities volition take their adjacent mayor, and immoderate volition measurement successful connected hotly contested ballot measures, including connected the contented of policing. There’s different governor’s contention successful New Jersey, too. Here is what to ticker successful immoderate of the cardinal contests that volition supply the astir elaborate and textured look yet astatine wherever voters basal much than 9 months into the Biden administration:

The Virginia contention is seen arsenic a bellwether

Democrats person won Virginia successful each statesmanlike contention since 2008. Last year, it wasn’t peculiarly close. Mr. Biden won by 10 percent points.

But Virginia besides has a past of bucking the enactment of a caller president — the authorities swung to the G.O.P. successful 2009, during erstwhile President Barack Obama’s archetypal twelvemonth successful bureau — and Republicans anticipation Mr. Youngkin has recovered a look for occurrence successful the post-Trump era.

To prevail, Mr. Youngkin needs to chopped into the margins successful suburban Northern Virginia, wherever voters person made the authorities progressively Democratic, portion besides turning retired a Republican basal that remains motivated by Mr. Trump.

His playbook has focused heavy connected education, attacking Mr. McAuliffe for a statement remark that parents should not beryllium directing what schools thatch and capitalizing connected a broader blimpish question against schools teaching astir systemic racism. The result: Education was the apical issue successful the race, according to an October Washington Post poll, giving Republicans the borderline connected a taxable that has traditionally favored Democrats.

Mr. McAuliffe has aggressively linked Mr. Youngkin to Mr. Trump, who endorsed the Republican but ne'er traveled to Virginia to run for him. If Mr. Youngkin loses, it volition showcase the G.O.P.’s ongoing situation successful being linked to Mr. Trump, adjacent with him disconnected the ballot. But if Mr. McAuliffe loses, it would intensify unit for Democrats to make a new, proactive message.

In the New Jersey governor’s race, Democratic incumbent Phil Murphy is up for re-election. Polls person showed Mr. Murphy ahead, but Mr. Biden’s weakening occupation support standing — which stood astatine 43 percent successful a caller Monmouth canvass — successful the solidly Democratic authorities are a origin of concern. The results volition beryllium watched for grounds of however overmuch of that erosion successful Mr. Biden’s enactment has seeped down-ballot.

Big mayoralties: Boston, Buffalo, Atlanta and more

It is not the biggest metropolis with a mayor’s contention connected Tuesday, but the City Hall conflict successful Buffalo, N.Y., whitethorn beryllium the astir fascinating.

India Walton, who would beryllium the archetypal socialist to pb a large American metropolis successful decades, defeated the incumbent Democratic mayor, Byron Brown, successful the June primary. But Mr. Brown is present moving a write-in campaign.

Ms. Walton has won the backing of progressives, specified arsenic Representative Alexandria Ocasio-Cortez, and immoderate enactment leaders, similar Senator Chuck Schumer, but different salient Democrats person stayed neutral, astir notably Gov. Kathy Hochul, a lifelong nonmigratory of the Buffalo region.

Policing has been a large issue. Though Ms. Walton has distanced herself from wanting to trim constabulary funding, Mr. Brown attacked her connected the contented successful a television ad.

In Boston, the runoff puts 2 metropolis councilors, Michelle Wu and Annissa Essaibi George, against each other, with Ms. Wu moving arsenic the progressive. Ms. Wu, who is backed by Senator Elizabeth Warren of Massachusetts, finished successful archetypal spot successful the primary.

In New York City, Eric Adams, the borough president of Brooklyn and a Democrat, is expected to triumph the mayor’s contention and has already fashioned himself arsenic a nationalist figure. “I americium the look of the caller Democratic Party,” Mr. Adams declared aft his June superior win..

In Miami, Mayor Francis Suarez, a uncommon big-city Republican mayor, is heavy favored to triumph re-election and is lined up to go the president of the U.S. Conference of Mayors, giving him a nationalist platform.

The aboriginal of policing is beforehand and center

One recurring taxable successful municipal races is policing, arsenic communities grapple with the “defund the police” slogan that swept the state pursuing the constabulary sidesplitting of George Floyd past year. The statement is raging wrong the Democratic Party implicit however overmuch to overhaul instrumentality enforcement — and implicit however to speech astir specified an overhaul.

Perhaps obscurity is the contented much cardinal than successful Minneapolis, the metropolis wherever Mr. Floyd was killed, sparking civilian unrest. Voters determination volition determine connected a measure to regenerate the troubled Minneapolis Police Department with a caller Department of Public Safety..

Mayor Jacob Frey, who is up for re-election, has opposed that measurement and pushed for a much incremental approach. His challengers, among them Sheila Nezhad, privation a much assertive approach.

Policing is simply a cardinal contented not lone successful the Buffalo mayor’s race, but besides successful mayoral contests in Seattle, Atlanta and successful Cleveland, wherever an amendment that would overhaul however the city’s constabulary section operates is connected the ballot arsenic well.

The mayor’s contention successful Cleveland puts Justin Bibb, a 34-year-old governmental newcomer, against Kevin Kelley, the City Council president. Mr. Bibb supports the constabulary amendment and Mr. Kelley opposes it.

House races and Pennsylvania’s tribunal battle

There are 2 peculiar elections for House races successful Ohio. A Cuyahoga County assembly member, Shontel Brown is expected to triumph a heavy Democratic spot successful Cleveland. Mike Carey, a longtime Republican ember lobbyist, is favored successful a territory that sprawls crossed a twelve counties.

Mr. Carey faces Allison Russo, a Democrat endorsed by Mr. Biden. Mr. Carey’s borderline successful a spot that Mr. Trump carried by much than 14 points past twelvemonth volition beryllium different invaluable indicator of the governmental environment.

In Florida, a superior is being held for the spot of Representative Alcee Hastings, who died earlier this year. The victor volition beryllium favored successful a January peculiar election.

The lone statewide races happening successful Pennsylvania connected Tuesday are for the courts. The astir intimately watched contention is for the authorities Supreme Court, which features 2 appeals tribunal judges: a Republican, Kevin Brobson, and a Democrat, Maria McLaughlin. Democrats presently clasp a 5-2 bulk connected the court, and the spot being vacated was held by a Republican, truthful the effect volition not plaything control.

But millions of dollars successful advertizing are pouring into the state, a motion not conscionable of the expanding politicization of judicial contests, but besides of the state’s relation arsenic a apical statesmanlike battleground.