11:55 p.m. ET
Approximately 2,000 votes separate Trump and Cruz in Missouri, making the state too close to call.
11 p.m. ET
Sen. Ted Cruz addressed his supporters, commending Marco Rubio for his campaign and urging Rubio's supporters to line up behind him.
"After tonight, America now has a clear choice going forward," Cruz said, implying there's no viable path forward for John Kasich. "To those who supported Marco, who worked so hard, we welcome you with open arms."
He also slammed the front-runner, Donald Trump, without naming him. "Do you want a candidate shares your values," he asked, or "a candidate who has spent decades opposing your values?"
Trump, he said, "may be the one person on the face of the Earth who Hillary Clinton can beat in the general election."
10:30 p.m. ET
Donald Trump addressed his supporters from his Florida resort, Mar-a-Lago, where he reiterated most of his standard talking points. "Apple and all of these great companies will be making their product in the United States, not in China," he said.
He also noted how much money was spent on attack ads against him in Florida. "Nobody has ever in the history of politics received the negative advertising that I have," he said. "My numbers went up, I don't understand it."
10 p.m. ET
CBS News projects that Donald Trump is the winner in North Carolina.
9:55 p.m. ET
John Kasich thanked his supporters in Berea, Ohio on Tuesday night after winning his state. As he has for most of his campaign, he struck a positive note.
"I will not take the low road to the highest office in the land," he said. "I think we can rally the people in Washington because I'm going to remind them that before we're Republicans and Democrats, we're Americans."
At the start of his remarks, a Trump supporter interrupted Kasich. The governor said, "When you went to college in the 1970s, you appreciate a good, peaceful protest every once in a while."
9:46 p.m. ET
CBS News projects Donald Trump is the winner in Illinois.
9:02 p.m. ET
The CBS News exit polling shows how Kasich won in Ohio:
Kasich won with a boost from late deciders. Twenty-three percent of voters made their candidate choice in the last few days, and they went for Kasich over Trump by a wide margin, 53 percent to 27 percent.
Kasich won among college graduates, higher income voters and all age groups. He won among both women (46 percent to 33 percent for Trump), and, by a smaller margin, men (43 percent to 40 percent for Trump).
Kasich won moderates (57 percent to 34 percent for Trump), and narrowly beat Trump among white evangelicals and conservatives.
Thirty-seven percent said that "shares my values" was the most important quality they were looking for, and 62 percent of them voted for Kasich. In addition, the economy was the top issue on voters' minds, and 50 percent of them chose Kasich.
In contrast to Trump's supporters, Kasich won among those voters who oppose banning Muslims, who want to offer illegal immigrants a chance to apply for legal status, and who describe themselves as dissatisfied rather than angry.
If Donald Trump and Hillary Clinton are the candidates in November, 43 percent said they would seriously consider voting for a third party candidate and 51 percent would be satisfied with that choice. Among Kasich supporters, 70 percent said they might vote for a third party candidate.
8:53 p.m. ET
CBS News projects that Ohio Gov. John Kasich will win Ohio.
Additionally, CBS News now characterizes the Republican race in North Carolina as learning towards Donald Trump. Earlier, the race was considered a toss up between Trump and Ted Cruz.
8:30 p.m. ET
Marco Rubio suspended his campaign Tuesday evening after a brutal loss in his home state of Florida to Donald Trump. In his remarks, Rubio referenced the anger fueling Trump's campaign without explicitly naming the front-runner.
"While this may not have been the year for a hopeful and optimistic message, I still main hopeful and optimistic about America," he said. He urged voters, "Do not give into the fear, do not give into the frustration. We can disagree about public policy... but we are a hopeful people, and we have every right to be hopeful."
8:25 p.m. ET
According to the CBS News Florida exit poll:
Trump ran well ahead of Rubio and Cruz among men (52 percent for Trump, 23 percent for Rubio, 17 percent for Cruz). The race was much closer between Trump and Rubio among women.
Trump ran well ahead among white voters (51 percent for Trump, 23 percent Rubio, 17 percent Cruz). Nine percent of Republican primary voters are Cuban, and Rubio lead Trump among those voters, 68 percent to 14 percent. Among other Hispanic voters, Rubio ran ahead of Trump, 45 percent to 35 percent.
Trump has big leads among those Republican voters who say that illegal immigrants working in the U.S. should be deported (38 percent); those who support a temporary ban on Muslims who are not U.S. citizens (64 percent); among those who are angry at the way the federal government is working (40 percent); among those who feel betrayed by politicians from the Republican Party (60 percent); and among those who want the next president to be from outside the political establishment (52 percent).
Trump runs behind Rubio and Cruz among voters who say that "shares my values" is the most important candidate quality they were looking for. Trump runs ahead among those who say that the want a candidate who can win in November. He also runs head among those who want someone who "tells it like it is" and those who want someone who can bring needed change.
8 p.m. ET
CBS News projects that Donald Trump will win the GOP primary in Florida, where polls are now closed. This is a devastating blow to Florida Sen. Marco Rubio. Florida is a winner-take-all state, meaning Trump wins all of the state's 99 delegates.
Polls have also closed in Illinois, and Trump is leading there.
In Missouri, where polls are now closed, it's currently a toss-up between Donald Trump and Ted Cruz.
7:57 p.m. ET
More from the CBS News Ohio Republican exit poll:
Fifty-five percent of Republican primary voters said that trade with other countries takes away U.S. jobs. Trump leads Kasich, 45 percent to 39 percent, among those voters. Another 33 percent said that trade creates more U.S. jobs, and Kasich leads Trump among those voters, 49 percent to 30 percent.
Forty percent said that most illegal immigrants working in the U.S. should be deported. Among those voters, Trump leads Kasich, 58 percent to 21 percent. Fifty-four percent said that illegal immigrants should be offered a chance to apply for legal status, and Kasich leads Trump among those voters, 61 percent to 25 percent.
Sixty-five percent said that they support temporarily banning Muslims who are not U.S. citizens entering the U.S., and Trump leads Kasich, 50 percent to 30 percent, among those voters. Another 31 percent oppose banning Muslims. Among those voters, Kasich leads Trump, 72 percent to 15 percent.
Thirty-nine percent said they are angry about the way the federal government is working. Trump leads Kasich among those voters, 52 percent to 29 percent. Fifty-three percent said they were dissatisfied but not angry, and Kasich leads Trump among those voters, 52 percent to 31 percent.
Fifty percent said that they want the next president to be from outside the political establishment. Trump leads Kasich, 68 percent to 16 percent, among those voters. Another 43 percent said they want the next president to have experience in politics, and Kasich leads Trump among those voters, 74 percent to 7 percent.
7:45 p.m. ET
More from the CBS News North Carolina exit poll:
Trump and Cruz running about even among women. Trump is ahead among men by about 8 percent. Trump is running strongly among those without a college degree, especially among those who have never attended college.
Where Trump is strong:
Fifty-eight percent of Republican primary voters said that trade with other countries takes away U.S. jobs. Among those voters, Trump leads Cruz, 46 percent to 31 percent.
Twenty percent said they were falling behind financially. Trump leads Cruz among those voters, 47 percent to 29 percent.
Forty percent said that most illegal immigrants working in the U.S. should be deported. Among those voters, Trump leads Cruz, 52 percent to 35 percent.
Sixty-six percent said that they support temporarily banning Muslims who are not U.S. citizens entering the US, and Trump leads Cruz among those voters, 50 percent to 34 percent.
Forty percent said they are angry about the way the federal government is working; Trump leads Cruz, 52 percent to 30 percent, among those voters.
Fifty-six percent said that they want the next president to be from outside the political establishment, and Trump leads Cruz, 65 percent to 26 percent, among those voters.
Where Cruz is strong:
Thirty-six percent said that they consider themselves "very conservative." Cruz leads Trump among those voters, 52 percent to 35 percent.
Thirty-seven percent said that the candidate quality that mattered the most to them was someone who "shares my values." Cruz leads Trump, 56 percent to 12 percent, among those voters.
7:30 p.m. ET
Polls have closed in Ohio, where Ohio Gov. John Kasich is leading the Republican field. The governor, who has yet to take first place in a nominating contest, has said that he must win his home state in order to stay in the race.
Polls have also closed in North Carolina, where it's currently a toss-up between Donald Trump and Ted Cruz.
In Ohio, the economy is the top issue among Republican voters. Among those who said the economy is the top issue, most are voting for Kasich (52 percent) over Trump (35 percent). Among voters who say trade hurts U.S. jobs, Kasich and Trump are about even.
More than seven in 10 voters who are looking for a candidate with political experience are backing Kasich, while 68 percent of those who want an outsider are backing Trump.
Late deciders - those who made up their minds in the last few days - are breaking for Kasich (55 percent).
In North Carolina, white evangelicals (about six in 10 voters) are going for Trump. Cruz is getting the backing of those who say values in their top candidate quality. College educated voters going slightly for Cruz, while those without a college education are backing Trump.
6:15 p.m. ET
Exit polling shows that more than half of Florida Republican primary voters want the next president to have a background outside of politics:
6 p.m. ET
A closer look at exit polling from Ohio and Florida:
5:35 p.m. ET
The Republican exit polls asked voters, "If Donald Trump and Hillary Clinton were the candidates in November, would you: be satisfied with that choice or seriously consider voting for a third party candidate?
In Florida, three in 10 Republican primary voters said they'd consider voting for a third party candidate. In the other three states, four in 10 say they'd consider it.
5 p.m. ET
The economy is the top issue for Republicans in every state voting today, according to CBS News exit polling.
Tuesday's primaries in Ohio and Florida are sure to mark a turning point in the GOP race. Both large states award their substantial delegate counts on a "winner-take-all" basis, and front-runner Donald Trump could effectively lock down the nomination. Meanwhile, Tuesday may mark the end of the road for the campaigns of Florida Sen. Marco Rubio or Ohio Gov. John Kasich if they cannot claim victory in their respective home states.
- Tuesday's nomination contests: Where to find all the results
- CBS News Election Center
- Live updates: Democratic primaries
All told, there are 358 delegates from five different states at stake for the Republicans on Tuesday. Along with voters in Ohio and Florida, Republican voters in Illinois, Missouri and North Carolina are casting ballots Tuesday. Along with Trump, Rubio and Kasich, Texas Sen. Ted Cruz is also in the running.
In the three states where Republican voters were asked about trade (Illinois, North Carolina and Ohio) in the exit polling, more said U.S. trade with other countries takes jobs away from the U.S., rather than creates them.
Generally, when it comes to candidate qualities, most Republican primary voters said they are primarily interested in a candidate who shares their values.
As we've seen in earlier primaries, Republicans express dissatisfaction with the way the federal government is working. Many voters in these states say they are angry at the government.
Also, about half of Republican primary voters in these states say they feel betrayed by the Republican party. More voters are looking for an outsider as the next president rather than someone with political experience, but voters in Ohio are divided on this.
Polls close in Ohio and North Carolina at 7:30 p.m. ET, and they close at 8 p.m. ET in Florida, Illinois and Missouri.