Mamdani promised to bring New York City into an age of "relentless improvement" as he claimed victory in the mayoral race late Tuesday night.

He said his win was one for the working people of New York and reiterated his campaign promises on affordability.

"Let the words we've spoken together, the dreams we've dreamt together, become the agenda we deliver together," Mamdani said. "New York, this power, it's yours. This city belongs to you. Thank you."

To watch his full victory speech, click here.

"Hope over tyranny. Hope over big money and small ideas. Hope over despair. We won because New Yorkers allowed themselves to hope that the impossible could be made possible. And we won because we insisted that no longer would politics be something that is done to us. Now it is something that we do," Mamdani said. 

"Tonight we have stepped out from the old, into the new. So let us speak now with clarity and conviction that cannot be misunderstood about what this new age will deliver, and for whom. This will be an age where New Yorkers expect from their leaders a bold vision of what we will achieve rather than a list of excuses for what we are too timid to attempt. Central to that vision will be the most ambitious agenda to tackle the cost of living crisis that this city has seen since the days of Fiorello La Guardia," Mamdani said. 

He said his agenda includes: 

• Freezing rents for more than 2 million stabilized tenants
• Making buses fast and free
• Delivering universal child care across the city

"Years from now, may our only regret be that this day took so long to come," Mamdani said, promising "relentless improvement." 

Mamdani promised to hire thousands of new teachers. 

"Safety and justice will go hand in hand as we work with police officers to reduce crime and create a Department of Community Safety that tackles the mental health crisis and homelessness crises head on," Mamdani said. "Excellence will become the expectation of government, not the exception."

"To every New Yorker whether you voted for me, for one of my opponents, or felt too disappointed by politics to vote at all, thank you for the opportunity to prove myself worthy of your trust," Mamdani said. "I will wake each morning with a singular purpose - to make this city better for you than it was the day before." 

"There are many who thought this day would never come, who feared that we would be condemned to a future of less, with every election consigning us simply to more of the same. And there are others who see politics today as too cruel for the flame of hope to still burn. New York, we have answered those fears," Mamdani said. "Tonight, we have spoken in a clear voice. Hope is alive." 

Zohran Mamdani was greeted by raucous cheers as he spoke to his supporters Tuesday night. 

"For as long as we can remember, the working people of New York by the wealthy and the well connected that power does not belong in their hands," Mamdani said. "You have dared to reach for something greater. Tonight, against all odds, we have grasped it. The future is in our hands."  

"My friends, we have toppled a political dynasty. I wish Andrew Cuomo only the best in private life, but let tonight be the final time I utter his name as we turn the page on a politics that abandons the many and answers only to the few," he said. 

"New York, tonight you have delivered a mandate for change. A mandate for a new kind of politics. A mandate for a city we can afford, and a mandate for a government that delivers as exactly that." 

Gov. Kathy Hochul took to social media to congratulate Zohran Mamdani on his projected victory. 

"Just spoke to Mayor-Elect [Zohran Mamdani] and told him I'm looking forward to working together to make our city more affordable and livable. Congratulations to him and to every New Yorker who made their voice heard in one of the city's highest-turnout elections on record," Hochul wrote. 

Senate Minority Leader Chuck Schumer issued a statement congratulating Mamdani. 

"I congratulate Mayor-elect Mamdani on his well-earned and historic victory tonight. His campaign was relentlessly focused on the cost-of-living crisis, that Donald Trump has only made worse, and on finding ways to help working families, seniors, and young people build a life of dignity and economic security in New York City. I have worked collaboratively and productively with Mayor-elect Mamdani on a number of vital issues over the years — including delivering historic relief to our taxi drivers who were suffering under crushing and unfair debt — and I look forward to building on that partnership to keep New York City strong, fair, more affordable, and thriving," Schumer said.

In addition to electing Zohran Mamdani mayor, New York City voters decided other key races as well. 

Jumaane Williams won re-election as public advocate. 

Mark Levine won election as comptroller. 

Vanessa Gibson won re-election as Bronx borough president.

Antonio Reynoso was re-elected as Brooklyn borough president. 

Brad Hoylman-Sigal was elected Manhattan borough president. 

Donovan Richards was re-elected as Queens borough president. 

Vito Fossella was re-elected as Staten Island borough president. 

Alvin Bragg was re-elected as Manhattan DA. 

Click here for more election results. 

Andrew Cuomo spoke to his supporters Tuesday night after Zohran Mamdani was projected the winner of the New York City mayor's race. 

Cuomo called his supporters "New York patriots." 

"This campaign was the right fight to wage, and I am proud of what we did and what we did together. This campaign was to contest the philosophies that are shaping the Democratic party, the future of this city, and the future of this country," Cuomo said. 

Cuomo praised the large turnout of more than 2 million voters, saying he garnered more than 40% of the vote while running as an independent - the highest percentage, he said, in modern history. 

"We will not make the NYPD the enemy. We cherish our diversity, and we have no tolerance for discrimination of any kind by race, religion, sexual orientation or creed, and we will not tolerate any behavior that fans the flames of antisemitism," Cuomo said. "Our strength is our unity. Black, White, Brown, Christian, Muslim, Jewish, Buddhist, we are one. We are the family of New York. We believe in interconnection and mutuality and codependence, and you attack one of us, you attack all of us. That is what it means to be a New Yorker. No one and nothing will ever divide us. And this campaign was necessary to make that point - a caution flag that we are heading down a dangerous, dangerous road.

"We made that point, and they heard us, and we will hold them to it," he added. 

Cuomo offered his congratulations to Mamdani, and was greeted with a chorus of boos. 

"That is not right. That is not us. Tonight was their night, and as they start to transition to government, we will all help any way we can because we need our New York City government to work. We want it to work for all New Yorkers, because our city is the greatest city in the world, and we will unite for New York City because we love New York City," Cuomo said. 

Here's a breakdown of which New York City neighborhoods went for Zohran Mamdani in the New York City mayoral election. 

The turnout this election was very strong, with more than 2 million voter check-ins as of 9 p.m., including the record early voting turnout. It's the first time that's happened since 1969.

By way of comparison, the greatest number of votes ever cast in a New York City mayoral election was in a special election in 1950, when more than 2.6 million votes were cast - 2,626,476 votes to be exact, according to the Board of Elections. 

That special election was called after Mayor William O'Dwyer left office to serve as ambassador to Mexico as a scandal involving gambling swirled around City Hall and the NYPD. 

Vincent Impellitteri became acting mayor, and then went on to win the special election. 

When Zohran Mamdani occupies Gracie Mansion, he will be responsible for overseeing one of the biggest and most complicated bureaucracies in the world, impacting the lives of some 8.5 million New York City residents. 

We spoke with a political expert about what exactly the mayor can -- and can't -- do, particularly when it comes to raising taxes, influencing laws and freezing rent. 

"The mayor of New York City has enormous powers," said political expert J.C. Polanco, a professor at the University of Mount Saint Vincent in the Bronx. "Not only do they supervise a staff of over 300,000 people, a budget of over $120 billion, a GDP of $1.3 trillion -- that's bigger than 10 other countries. We're in the top 10 in the world. Consider 1 million kids in our public schools, 10 million people at any given time, 30,000 cops, it's a lot of power."

Mamdani is projected to have won with more than 50% of the vote, which is notable since the race was hotly contested among three candidates. 

If Mamdani did not win at least 50% of the vote, there may have been questions about whether or not he had a mandate from a majority of voters. 

By exceeding 50% of the vote, he is positioned to put that debate to rest, although no doubt he will continue to have his detractors. 

The Mamdani campaign wasted little time celebrating their victory. 

They posted a short video on social media, showing the perspective from inside a subway car as the doors open at the City Hall stop. 

"The next and last stop is City Hall," the subway announcer says. 

The crowd roared as New York City elected Zohran Mamdani as the next mayor of New York City. 

Mamdani ran on a promise to improve affordability for New Yorkers. 

Democratic socialist Zohran Mamdani's victory on Tuesday in the New York City mayoral race is already fanning the debate about the future of the Democratic Party and what his sudden political stardom could mean for next year's midterm elections. 

"We hope this is demonstrating a very powerful way forward," said Ashik Siddique, a national co-chair of the Democratic Socialists of America. "This election proves that democratic socialist ideas are very popular." 

Mamdani ran on promises to confront economic inequality and cost-of-living issues, vowing rent freezes for residents of rent-stabilized units, affordable housing construction, free — and faster — bus service, free childcare, city-owned grocery stores to address high food costs and tax hikes on the wealthy. 

Click here to read more.  

Zohran Mamdani, a self-proclaimed democratic socialist, will be New York City's 111th mayor, CBS News projects. His victory caps a closely watched campaign in which the little-known state assemblyman energized voters with his focus on making America's largest city more affordable.

Click here for more on Mamdani's meteoric rise to become the 111th mayor of New York City.   

Curtis Sliwa addressed his supporters at around 9:20 p.m.

He thanked the more than two million voters who turned out to vote. 

"This has always been us versus them. From the time I declared my candidacy, the masters of the universe, the billionaires decided that I should not have the right to represent all of you. To be the voice of the voiceless, the working class people who are the backbone of this city," Sliwa said. 

"And then they bribed me. As much as $10 million," Sliwa said. "I'll never forget my great wife Nancy was listening to that final call when a person said to me 'Come on Curtis, everybody has a price.' Well guess what, we don't have a price. You can't buy us, rent us, lease us. We are not for sale. We are the people."

Sliwa said he wishes the future mayor good luck. 

"If he does well, we do well," Sliwa said. 

Voter turnout was steady at Co-Op City in the Bronx on Tuesday. It's a precinct that Andrew Cuomo took in the Democratic primary and is looking to run up his margin over Zohran Mamdani.

When CBS News New York's Tony Aiello visited, Cuomo had one volunteer handing out literature while Mamdani had a table with four volunteers in place.

Many voters said issues like affordability, housing, transit and public safety were on their minds as they headed to the polls.

None, however, mentioned experience – a major focus of Cuomo's campaign.

"That's about making the government work, which is what I have done all my life. That's how you really make change. You make change by understanding how to run the government," Cuomo said.

Polls have now closed in the New York City mayoral race. 

While the race for mayor is getting a lot of attention, many other races and ballot proposals are being decided. 

CLICK HERE for complete election results across New York City. 

The New York City Board of elections says voter turnout has surpassed two million votes. 

It's the first time that's happened since 1969. 

Record turnout was in 1950 with 2.6 million votes cast. 

Voters in line by 9 p.m. are eligible to vote. 

CBS News New York's Marcia Kramer said President Trump's endorsement of Andrew Cuomo was "a calculated decision." 

"Here's why," she explained. "It came at the last moment and it sent a message to Republicans who always vote on Election Day, or often vote on Election Day, so it would get their vote out. And at the same time it came late enough that it didn't antagonize Democrats who don't like Trump very much. So I think it was a brilliant move on Trump's part to help Cuomo and to try not to hurt him." 

Curtis Sliwa remains defiant in his bid to become the next mayor, despite low poll numbers and limited resources. The 71-year-old Republican crisscrossed the city Tuesday to make his final pitch to voters, and give down-ballot Republicans a boost in their City Council races. 

"It's a fight to the finish, it's a fight for residential neighborhoods, and it's fight to get our Republicans elected so that we can balance what the [Democratic Socialists of America] has in terms of their influence on the City Council," he said. 

Sliwa built his campaign on public safety, quality of life and animal welfare, but many members of the GOP, including President Trump, refused to back him, insisting his candidacy improves Mamdani's chances of winning. 

"In every one of the 350 neighborhoods, people agree with me that this is not an election that's going to be determined by the billionaires, insiders or influencers, or the political elite. This will be determined by the people, and they're certainly exercising their right to vote in an unprecedented way in a mayoral election," he said.

Andrew Cuomo has been the clear frontrunner in all four of his previous general election campaigns, never winning less than 54% of the vote.

Now, he's in an unusual position – trailing Zohran Mamdani in the polls.

He's also trying to avoid repeating history; his father, Mario Cuomo, ran as a third-party candidate in 1977 and lost to Ed Koch. Newspapers at the time noted Koch had been an "obscure" legislator just 10 months prior, not unlike Mamdani.

"I'm feeling very good. I feel the momentum is on our side. If you watch the polls, they've all been moving to us. I've been on the street. I feel it from people," Andrew Cuomo said.

Meanwhile in New Jersey, voters are deciding a closely watched race for governor. Democrat Mikie Sherrill is taking on Republican Jack Ciattarelli to replace outgoing Gov. Phil Murphy in the Garden State. 

Much like the New York City mayoral election, President Trump and the issue of affordability are looming large over the race. 

Click here for live Election Night coverage from New Jersey. 

Three polling sites in Manhattan were targets of an "elaborate swatting attempt" on Election Day, police sources said. 

Locations in the West Village, Midtown and Washington Heights all received threats through the Board of Elections email system, according to sources. 

The threats were of a "terroristic nature," police sources said. 

Voting in New York City was not impacted, however, as residents went ahead and cast their ballots. 

The threats in New York City came to light after police in New Jersey responded to bomb threats at polling places in at least seven counties. 

While New York and New Jersey have two closely watched races for mayor and governor, respectively, voters across the country are hitting the polls this Election Day. 

One big issue on the ballot this election is Prop 50 in California. The controversial measure would redraw congressional district maps, potentially impacting the balance of power in the House.

CBS News is covering all the latest developments in their live blog here.

While President Trump opined many times on the New York City mayor's race during the campaign, saying he did not want Zohran Mamdani to win, it wasn't until Election Eve that he told voters to support Andrew Cuomo. 

"Whether you personally like Andrew Cuomo or not, you really have no choice. You must vote for him and hope he does a fantastic job," the president said in a Truth Social post. "A vote for Curtis Sliwa ... is a vote for Mamdani." 

Mr. Trump again said he would limit funds coming from the federal government to New York City if Mamdani is elected. 

Click here to read more. 

Outgoing New York City Mayor Eric Adams took to social media to urge New Yorkers to get out and vote before polls close. 

"Your vote is your power, New York City," Adams wrote. "Make sure you use your voice today and get to the polls by 9 PM!" 

Adams also shared pictures of himself casting his ballot. 

Former Mayor Bill de Blasio posted a selfie after he cast his ballot for Zohran Mamdani Tuesday. 

"One of the happiest votes I ever cast! What a beautiful day for NYC!" the former mayor wrote. 

Days before Election Day, Mayor Eric Adams announced he approved more than $300 million to hire 5,000 new police officers by 2028. 

The issue of NYPD headcount has been hotly contested in the mayoral campaign, with Mamdani saying he's not planning to hire more officers, and Cuomo and Sliwa promising to add thousands to the ranks. 

Adams said the funding puts the city "on a path to reach 40,000 police officers in the next three years — the highest number of police officers in 20 years."

It will be on the next mayor to implement such a move, however.

Click here to read more. 

We've heard from the candidates for months, but what do New Yorkers have to say about the race?

CBS News New York's Jessica Moore sat down with a group of voters for their take on some of the hot button issues.

The group was made up of eight voters -- six who said they already knew who they were voting for, and two who said they were still undecided.

They covered a range of topics from affordability to crime and public safety, weighing in on the candidates' policies and visions for the future of the city. 

CLICK HERE to watch their conversation on affordability, HERE for more on public safety and HERE on the issue of experience in the race.

Each of the candidates sat down with CBS News New York for in-depth interviews on "The Point with Marcia Kramer" over the past few months. 

Mamdani spoke extensively about his plan for public safety, including the creation of a Department of Community Safety, and answered questions about how exactly he plans to pay for his affordability agenda. Click here to watch the complete interview.

Cuomo also touched on the issue of safety, calling for 5,000 more NYPD officers and cracking down on e-bike violations, as well as his plan to build more affordable housing. Click here to watch the full conversation. 

Sliwa told Kramer he hopes to be seen as a combination of former Mayors Rudy Giuliani and Michael Bloomberg, calling himself the "law and order" candidate, who also has a passion for protecting animals. Click here to watch the complete interview.

Republican candidate Curtis Sliwa cast his ballot on Oct. 25, during the early voting period. 

Democrat Zohran Mamdani cast his ballot on Election Day in Queens. 

"It is time to finally respond with the urgency that New Yorkers deserve -- an urgency that reckons with these same New Yorkers having had to face rent hike after rent hike year after year, these same New Yorkers having to wait for buses that never come, these same New Yorkers that have to move out of this city when they want to raise a family," Mamdani said.   

"I feel the momentum is on our side. If you watch the polls, they've all been moving to us. I've been on the street. I feel it from people," Cuomo said as he voted with his family in Manhattan. 

The mayoral election has captured the attention of the city and the country. President Trump repeatedly weighed in on the race, and the candidates received high-profile endorsements from Congressional, state and city leaders. 

Mamdani has the support of House Minority Leader Hakeem Jeffries, Sen. Bernie Sanders, Rep. Alexandria Ocasio-Cortez and Gov. Kathy Hochul, among several other Democrats. 

Cuomo was endorsed by Mr. Trump, outgoing Mayor Eric Adams, former Gov. David Paterson and former Mayor Michael Bloomberg, as well as labor unions and faith leaders. 

Sliwa, meanwhile, is being backed by Reps. Mike Lawler and Elise Stefanik, along with former Mayor Rudy Giuliani. 

Mamdani and Cuomo stopped by their polling sites Tuesday morning to cast their ballots in the final hours of the race. Sliwa had already cast his during early voting. 

"It is time to finally respond with the urgency that New Yorkers deserve -- an urgency that reckons with these same New Yorkers having had to face rent hike after rent hike year after year, these same New Yorkers having to wait for buses that never come, these same New Yorkers that have to move out of this city when they want to raise a family," Mamdani said outside his polling location in Astoria, Queens, where he voted alongside his wife. 

"The record turnout is a good sign. I think it's going to be a record. And it's because New Yorkers are concerned. New Yorkers are concerned about New York," said Cuomo, as he voted alongside his family in Manhattan. 

"I have the people's support and, hopefully, when all the ballots are counted tonight, when all is said and done, I'll be the next mayor of the City of New York," Sliwa said at an appearance with his wife on the Upper West Side.

More than 1,748,698 check ins have been made as of 6 p.m., including early voting, the Board of Elections said. 

The most were in Brooklyn, with more than 570,000 check ins, followed by Manhattan, Queens, the Bronx and Staten Island, in that order. 

Voters in Rego Park, Queens told CBS News New York they showed up in order to have a say in the city's future. 

Meanwhile, three polling sites in Manhattan were targeted with threats on Election Day, but voting was not impacted, police sources said. Several polling locations across New Jersey also received threats early Tuesday morning. 

President Trump weighed in on the closely watched race for New York City mayor in an exclusive interview with 60 Minutes, again suggesting he may withhold federal funding to New York if Democratic candidate Zohran Mamdani is elected.

The 34-year-old Queens assemblyman has proposed policies he says address affordability in the city, like free child care, a rent freeze and free buses. 

The president said he thinks the young politician is a "communist" and "far worse than a socialist." 

"Some people have compared him to a left-wing version of you, charismatic, breaking the old rules. What do you think about that?" O'Donnell asked. 

"Well, I think I'm a much better looking person than him, right?" the president joked. 

Read more of the interview here. 

In addition to mayor and other city offices, New Yorkers will also decide on six ballot proposals. 

Three have to do with the City Council's role in land use decisions, another involves an Olympic sports complex on state land upstate, another would create a digital map of the city, and the last would move local election years in line with presidential elections. 

• Ballot Proposal 1: Amendment to Allow Olympic Sports Complex in Essex County on State Forest Preserve Land
• Ballot Proposal 2: Fast Track Affordable Housing to Build More Across the City
• Ballot Proposal 3: Simplify Review of Modest Housing and Infrastructure Projects
• Ballot Proposal 4: Establish an Affordable Housing Appeals Board with Council, Borough and Citywide Representation
• Ballot Proposal 5: Create a Digital City Map to Modernize City Operations
• Ballot Proposal 6: Move Local Elections to Presidential Election Years to Increase Voter Participation

New York City voters have until 9 p.m. to cast their ballots in the 2025 general election. 

Make sure to look up your designated polling location online HERE.

Reminder, Election Day locations can differ from early voting sites.

A CBS News exit poll finds cost of living is the top issue for voters, ahead of crime. 

Three in four New York City voters say the cost of housing is a major problem. Most call crime a problem, but fewer than half call it a "major" one.

A lot of this campaign has been defined by "change vs. experience" and that is reflected in what voters want in their next mayor. Those traits are at the top of a list of what the city's voters are looking for in a candidate. 

Democrat Zohran Mamdani's voters are more likely to be looking for someone who will bring needed change, while those backing life-long Democrat-turned-independent candidate Andrew Cuomo are looking for someone with experience. 

Events overseas have played a role in this local race. Most New York City voters overall say the candidates' positions on Israel were a factor in their vote, although it is a major factor for fewer than half. It is more of a factor for Jewish voters.

New York City voters are casting their ballots in several key offices, most notably the race for mayor. 

Incumbent Mayor Eric Adams is no longer seeking reelection after leaving the race in late September. 

Now, it's down to Democrat Zohran Mamdani, independent Andrew Cuomo and Republican Curtis Sliwa. 

New Yorkers are also voting for public advocate, comptroller, borough presidents, City Council seats and judges, along with six ballot proposals. 

CLICK HERE to find a sample ballot for your district.

Polls are open from 6 a.m. to 9 p.m. on Election Day in New York City. 

Voters in line before 9 p.m. should be allowed to cast their ballots. 

CLICK HERE to find your designated polling location.

Early voting set records for a non-presidential election in the city, according to the New York City Board of Elections. 

More than 164,000 voters hit the polls during the first weekend of early voting in the city alone, vastly outpacing the 31,176 votes cast during the same period in the 2021 mayoral election. That trend line continued throughout the early voting period. 

The BOE reported a total of 735,317 early voting check-ins over nine days, compared to 169,879 in the 2021 race.

Initial data showed voters over the age of 50 appeared to be outnumbering younger voters, who had dominated the Democratic primary. 

Since winning a stunning Democratic primary victory, Mamdani has consistently polled ahead of the pack. 

However, the latest poll released over the weekend showed his lead may be narrowing, down to just single digits over Cuomo. The Atlas poll, which surveyed over 1,500 people through Oct. 30, had Mamdani with 40% of the vote, Cuomo with 34% and Sliwa with 24%.

Three separate polls released late last week showed Mamdani with at least a 10-point lead over Cuomo, including an Emerson College poll that had Mamdani at 50%, Cuomo at 25% and Sliwa at 21%.

A poll released last Monday from Suffolk University Boston also found Cuomo was closing the gap. The poll showed 44% of those surveyed in favor of Mamdani, followed by 34% for Cuomo and 11% for Sliwa. A similar poll from Suffolk University Boston in September had Mamdani with double that lead, ahead of Cuomo by 20 points.

Another poll released last month showed a neck-and-neck race between Mamdani and Cuomo if Sliwa were to drop out - something the Republican has repeatedly dismissed.

A CBS News poll in September, before Mayor Adams left the race, found affordability was top of mind for New York City voters in this election. It showed 37% of likely voters said the cost of living was their most important issue in the race, followed by 31% who said crime and safety.

CBS News New York will have live updates as polls close and the results start coming in. 

This live blog will also be updated throughout Election Night with the latest from the candidates, voters and political experts.

Watch CBS News New York at 8 p.m. when polls close in New Jersey, followed by special election night coverage beginning at 9 p.m.

Then, we'll have even more expert analysis on CBS News New York at 11 p.m.