9:17 p.m. CBS News estimates that John Kasich will come in second to Donald Trump in the GOP primary.
"Governor Kasich is now the leading governor in the race and the only one with a realistic chance at the nomination," Kasich senior strategist John Weaver said in a statement. "He showed that a conservative with a positive message will succeed and, in fact, that's the only way for Republicans to win the White House. As the governor of Ohio he knows how to do it."
Kasich's campaign said he will leave for South Carolina Thursday night, and that he is now poised to "accumulate delegates in the early primary calendar before winning Michigan and taking the nomination battle to the Midwest, the home turf where he will win the nomination."
9:13 p.m. Despite finishing far outside of the top three candidates in New Hampshire, Carly Fiorina told supporters Tuesday, "We are going to keep going."
Fiorina added her supporters have "given us wind in our back." With 24 percent of votes counted, Fiorina is in second to last place with just 4 percent of the vote.
8:44 p.m. Some more analysis from the exit polls:
When asked about their view of the way the federal government is working, 48 percent of Republican New Hampshire primary voters were dissatisfied, but not angry, and 40 percent were angry. Of those who said they were dissatisfied or angry, 32 percent voted for Trump followed by 15 percent for Kasich.
Almost half of Republican primary voters (46 percent) said they feel betrayed by politicians from the Republican Party and of those, 32 percent backed Trump. Trump took the largest share of support from both men (34 percent) and women (29 percent). When asked about the most important issues facing the country, economy was seen as the most important. Of those who see that as the most important issue, 27 percent voted for Trump and 24 percent for Kasich.
Trump is also the top candidate choice for the other three issues: Immigration (50 percent), Terrorism (27 percent), and government spending (31 percent).
Trump did very well among Republican New Hampshire primary voters who want to see illegal immigrants deported: 46 percent voted for him. Of the 66 percent of Republican voters who support a temporary ban on Muslims entering the U.S, 42 percent back Trump. About a quarter of those who oppose a ban voted for Kasich.
8:40 p.m. Trump had a strong showing among late deciders as well as first-time primary voters. He also did better than expected among those voters who consider electability as key factor in their voting decision.
LATE DECIDERS FOR TRUMP AND KASICH: John Kasich and Donald Trump both appear to have benefitted from the more than 45 percent of Republican primary voters who chose a candidate at the last minute. Among those who decided in the last few days about 21 percent broke for Kasich while Trump received 20 percent of the vote.
FIRST TIME VOTERS SMALL IN NUMBER, BUT TRUMP WINS THEM: Only about 14 percent are voting in a Republican primary for the first time. Thirty-four percent voted for Trump -- but he also won 31 percent of voters who have previously voted in a primary.
TRUMP HAS A STRONG SHOWING AMONG THOSE WHO CONSIDER ELECTABILITY A KEY FACTOR: Only 12 percent of GOP primary voters focused on electability as a key factor in making their decision today. While it isn't a critical factor among most Republicans, among those who place a high value on it Rubio won with 33 percent of the vote, followed by Trump with 29 percent of the vote.
In Iowa, Rubio also won those voters who most valued a candidate who could win in November. GOP voters are far more interested in having a nominee who shares their values (35 percent), is capable of bringing about change (29 percent) or one who tells it like it is (22 percent). Trump was the top choice of both voters who want a change candidate and those who want a candidate who speaks his or her mind.
8:22 p.m. John Kasich is now leading the battle for second place in the New Hampshire Republican primary.
8:20 p.m. Trump's victory in New Hampshire can be explained in part by the fact that he won almost every key segment of GOP primary voters including independents, conservatives, and moderates. He also nearly tied Cruz when it comes to support among white evangelicals.
INDEPENDENTS: Independents are about 42 percent of the New Hampshire GOP primary electorate today, lower than the 47 percent in 2012, and slightly higher than the 37 percent in 2008. In Iowa last week, just 20 percent were independents. Trump won this group with 32 percent of the vote, followed by Kasich with 18 percent of the vote.
CONSERVATIVES/MODERATES: New Hampshire Republican voters are conservative, but just about 27 percent identify as very conservative -- far fewer than the 40 percent who did so in the Iowa caucus. Trump won the backing of those who describe themselves as very or somewhat conservative (65 percent), followed by Cruz (34 percent) and Rubio (28 percent). Almost three quarters of Republicans (72 percent) identify as conservative this year, up from 53 percent in 2012.
Interestingly, Trump also won moderates voters who make up just more than a quarter of the New Hampshire GOP. Results show that moderates broke for Trump (30 percent) and Kaisch (27 percent).
EVANGELICALS: Evangelicals are less of a factor in New Hampshire than they were last week in Iowa. White evangelicals made up about 23 percent of New Hampshire voters today (compared to 62 percent in Iowa). Whereas Cruz won this group in Iowa, he only did one percent better than Trump among this group of voters in New Hampshire Tuesday (Cruz received 24 percent of their votes and Trump 23 percent).
8:00 p.m. CBS News projects that businessman Donald Trump will win the New Hampshire Republican primary and Sen. Bernie Sanders, I-Vermont, will win the Democratic primary.
There is now a four-way tie for second place between John Kasich, Jeb Bush, Marco Rubio and Ted Cruz.
All polls in the state are now closed.
7:30 p.m. Voters in New Hampshire are casting their ballots before the last polling stations in the state close at 8 p.m. ET. If polls are correct, businessman Donald Trump is poised to sweep the New Hampshire primary with a clear lead over his rival Republicans.
Trump has a double-digit lead over his rivals in most polls, making the most interesting race of the night who will come in second place. There is a tight race between several candidates who would be considered part of the GOP establishment, including Ohio Gov. John Kasich, Florida Sen. Marco Rubio and former Florida Gov. Jeb Bush.
Texas Sen. Ted Cruz - who won the Iowa caucus a week ago - and New Jersey Gov. Chris Christie are also vying to stay in the mix, as well as former Hewlett-Packard CEO Carly Fiorina.
CBS News exit polls show that nearly half of New Hampshire Republican primary voters -- 46 percent -- made their decision on who to vote for within the last few days. About one-fifth, 22 percent, say they made their decision Tuesday.
One exit poll statistic that probably spells good news for a big Trump victory is this: Two third of Republican primary voters, 66 percent, support a temporary ban on Muslims entering the U.S. - something Trump proposed in December.
About half (48 percent) of Republican primary voters want a candidate with some political experience, while the other 47 percent would like the next president to be outside the political establishment. In Iowa, the majority of those who sought an outsider supported Trump. Of those seeking a candidate with experience, Iowa voters supported Rubio and Cruz.
Thirty percent of voters rate the economy and jobs as their top issue, more than those who said it was government spending (27 percent) and terrorism (25 percent).
And one issue which has been a point of contention within the race for many of the GOP candidates, especially for Marco Rubio, ranks much lower as a concern: only 15 percent of GOP respondents chose immigration as the most important issue.
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