10:30 p.m.Speaking at a victory rally in New York City, Clinton thanked supporters for her victory in New York and said Tuesday's results are proof that "there's no place like home."
"We've won in every region of the country," she added, a clear reference to Sanders' claim that she is leading in the delegate race because of her victories in the South. "From the north to the south to the east to the west, but this one's personal!"
Meanwhile, at a brief press avail upon landing in Burlington, Vt., Sanders congratulated Clinton on her victory but looked forward to next week's contests in Pennsylvania, Connecticut, Maryland, Rhode Island and Delaware, saying he and his team "look forward to winning a number of those states."
"Today we took Sec. Clinton on in her home state of New York and we lost," he said. "I congratulate Sec. Clinton on her victory."
Sanders also expressed "concern" over "the voting process" in New York, where voting irregularities were reported. "I hope that that process will change in the future and I'm not alone about my concerns," he said.
9:57 p.m.As the race was called for Clinton, the Empire State Building in New York turned blue in response:
9:45 p.m.Just minutes after the New York primary was called, Clinton tweeted to thank her supporters:
9:40 p.m. CBS News projects that Hillary Clinton wins the New York primary.
9:25 p.m. While the Democratic primary is still too close to call, here are some findings from the CBS News exit poll:
Clinton ran more strongly among women than men. Overall, she was supported by 57 percent of women voters but only 45 percent of men. Among white voters, she received 50 percent of women's votes and 39 percent of men's.
Sanders received a majority of support from white voters (54 percent to 45 percent for Clinton). Still, as she has in other states, Clinton ran strongly among nonwhites: she took 63 percent of their vote. She beat Sanders 71 percent to 28 percent among African Americans and 59 percent to 41 percent among Hispanics.
Repeating a pattern from the entire primary season, Sanders ran very strongly among young people, getting 85 percent of the votes of those under 25 and 61 percent of the votes of those 25 to 29. Clinton ran well ahead among voters over 45 (61 percent to 38 percent for Sanders). Fifty-nine percent of Democratic primary voters were over age 45.
Sanders won by a large margin among Democratic primary voters who said that they consider themselves very liberal (64 to 36 percent), but Clinton ran ahead among voters who said they were somewhat liberal or moderate who, combined, made up 67 percent of primary voters.
After a primary in which gun control featured prominently, 56 percent of primary voters said that Clinton would do a better job handling gun policy; 39 percent said that Sanders would.
New York Democrats were split on whether foreign trade helps or hurts U.S. jobs. Sanders ran better among voter said that trade hurts U.S. jobs, but not by as large a margin as in some previous primaries (57 percent for Sanders to 42 percent for Clinton). Sixty-four percent of Democratic primary voters said that Wall Street does more to hurt the U.S. economy ,and Sanders got 59 percent of the votes of this group. Clinton's 41 percent vote share among this group is a bit surprising, given the frequent emphasis Sanders has placed on this issue.
Only 9 percent of primary voters said they were scared about a Clinton presidency; 10 percent were scared about a Sanders presidency. Almost as many New York primary voters said they were excited about a Clinton presidency (21 percent) as a Sanders presidency (25 percent).
9:21 p.m.With less than 10 percent of the vote in, here's how many votes each candidate currently has:
9 p.m.New York polls are now closed across the state. CBS News projects that Hillary Clinton is leading Bernie Sanders in New York.
8:49 p.m.With just minutes to go until the New York polls close, here's where the delegate battle between Clinton and Sanders currently stands:
5:16 p.m.As early exit polling begins rolling in, here are some key takeaways thus far:
Democratic primary voters were asked whether Wall Street does more to help or hurt the U.S. economy. Twenty-nine percent of Democratic primary voters said it does more to help, while 64 percent said it does more to hurt the economy.
New York primary voters are split on the effects of international trade, with 41 percent saying that it creates more U.S. jobs and 40 percent saying that it takes away jobs.
Sixty-eight percent of Democratic primary voters said that the Democratic campaign has mostly energized the party, while 27 percent said that it has divided the party.
The most important issue to Democratic primary voters is jobs and the economy (35 percent), followed by income inequality (28 percent) and health care (20 percent).
5:13 p.m. All eyes are on New York today as voters continue heading to the polls across the state. It's the first big state to vote in two weeks and could help determine when -- and whether -- front-runner Hillary Clinton is able to wrap up the Democratic nomination over Vermont Sen. Bernie Sanders. Polls close across the state at 9 p.m. ET.
Early exit polling finds that Democratic voters think Clinton has run the more "unfair" campaign: asked campaign fairness, 49 percent said Clinton's campaign was more unfair, compared with 32 percent who named Sanders.
Still, more than two-thirds of Democrats said they expect Clinton to win: 70 percent named her as the likely nominee, compared with 28 percent for Sanders.
For Democrats, New York has 247 delegates which are allocated proportionally. According to CBS News' latest count, Clinton has 1,755 delegates (including superdelegates), with 2,383 required to win the nomination. Sanders has 1,060 delegates.
The New York primary has seen both candidates taking a much more contentious tone: Sanders, in particular, has picked up his attacks on Clinton, saying he is "tired" of the "negativity" of her campaign. The pair met for a debate last Thursday in Brooklyn, dubbed the "Brooklyn Brawl" for how many sparks flew on stage between Clinton and Sanders.
A CBS News Battleground Tracker poll released Sunday found Clinton leading Sanders by 10 points, 53 percent to 43 percent.
Follow here for live updates and exit polling data throughout the night.
Stony Brook University political science professor Stanley Feldman contributed to this story.