12:41 a.m. Trump is the winner of the Vermont primary, denying Kasich his only shot at a Super Tuesday victory.
11:19 p.m. Marco Rubio can officially notch one win on Super Tuesday: CBS News has him winning the Minnesota primary.
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- Live updates from the Democratic race
11:12 p.m. Here's a bit from Cruz's victory speech, where he celebrated his victories with a round of mudslinging at Trump.
"So long as the field remains divided, Donald Trump's path to the nomination remains more likely," Cruz told supporters gathered at the Redneck Country Club in Stafford, Texas. "And that would be a disaster for Republicans, for conservatives and for the nation."
11:05 p.m. Rubio, who spoke earlier in the evening, is now leading in Minnesota.
10:55 p.m. Former neurosurgeon Ben Carson is still in the race and told supporters in Maryland tonight that he has no plans to go anywhere.
Carson said he is "not ready to quit," and that the system is "rotten to the core."
10:31 p.m. Trump picks up his sixth Super Tuesday state with a win in Arkansas.
10:10 p.m. Instead of a victory party, Trump opted for a press conference in Florida. He just wrapped up and the clear message tonight was that he will unify the party.
"I think we're going to be more inclusive, I think we're going to be more unified, and I think we're going to win in November," he said, pointing to the high turnout on the Republican side.
That was also the message from New Jersey Gov. Chris Christie, who recently endorsed Trump and introduced him at the press conference.
"Tonight is the beginning of Donald trump bringing the Republican Party together for a big victory this November," he said.
He congratulated Cruz for his victory in Texas, but mocked Rubio for failing to win a single state so far. He blamed it on Rubio's negative attacks in the past few days.
"I always liked Marco until about a week ago when he decided to go hostile," Trump said. "He decided to become Don Rickles but Don has a lot more talent."
9:27 p.m. The Vermont primary is still a battle between Trump and Kasich, but here's a breakdown of some of the Republican vote there:
9:16 p.m. Here's a look at how Cruz won his home state:
9:12 p.m.He has yet to win a state on Super Tuesday - although he is battling Trump for the top slot in the Vermont GOP primary - but Kasich said he has "absolutely" exceeded expectations for Super Tuesday.
His claim is that he'll have home-court advantage in Mississippi and Michigan, which vote next Tuesday, and promised to beat Trump in his home state of Ohio on its March 15 primary.
9:08 p.m. We're now projecting Cruz as the winner of the Oklahoma primary.
9:02 p.m. CBS News now projects that Cruz is the likely winner of the Oklahoma primary.
9:00 p.m. Cruz is the winner of the Texas primary, CBS News projects.
8:55 p.m.Here's a look at how Trump edged out Rubio to win the Virginia primary:
8:45 p.m. CBS News projects Trump is the winner of the Virginia primary.
8:43 p.m.In six of the exit polls (Alabama, Arkansas, Georgia, Tennessee, Texas, Virginia) voters were asked how satisfied they would be if Trump, Cruz, or Rubio won the nomination. In all of these states about three out of four Cruz and Rubio voters said they would be dissatisfied if Trump is the nominee.
About six in 10 Trump voters said they would be dissatisfied if either Cruz or Rubio is the nominee.
Cruz and Rubio voters would be unhappy with Trump as the Republican candidate in November. A majority of Trump voters would be unhappy with any other candidate getting the nomination. Is this a problem for the Republican party in the general election?
8:30 p.m. Arkansas is a toss up between Trump and Cruz.
8:13 p.m. Trump is now leading in the Virginia primary.
8:00 p.m. CBS News projects that Trump is the winner in three more states: Alabama, Massachusetts and Tennessee. Cruz is leading in Oklahoma.
7:35 p.m. Trump is currently leading the Republican primary in Georgia with 40 percent of the vote. He is projected as the winner there. Cruz and Rubio are deadlocked for second place, with 23 percent and 22 percent respectively.
Nearly two-thirds of voters in Georgia (60 percent) are evangelicals. Trump is winning with 41 percent of their votes, compared to Cruz with 26 percent and Rubio at 20 percent.
Eight in 10 Georgia Republican primary voters identify as conservative, and Trump leads that group as well with 39 percent of the vote. Next up is Cruz with 25 percent and Rubio with 21 percent.
When asked which of the candidates would best handle Supreme Court nominations, voters are tied between Cruz and Trump, each getting 32 percent.
Interestingly, Trump is perceived as having run the most unfair campaign - 38 percent of voters said so. Just 28 percent said Cruz ran the most unfair campaign. Late deciders - voters who made up their minds in the last few days - are split between Cruz (31 percent) and Rubio (30 percent).
Rubio is winning among the 12 percent of voters who say they care most about picking a candidate who can win in November. He earned 44 percent of their votes. Among the 31 percent that want a candidate who shares their values, 35 percent picked Cruz. And among the 18 percent of voters who want a candidate who tells it like it is and the36 percent of voters who want a candidate who can bring change, Trump won both groups with 79 percent and 46 percent of those respective groups.
Trump's support decreases as education level increases. Rubio has the opposite impact: his support increases as education increases: Trump won 53 percent of voters who have a high school education or less, 41 percent of those with some college, 37 percent of college graduates, and 28 percent of those with postgraduate degrees. Rubio won 13 percent of those with a high school education or less, 20 percent of those with some college, 25 percent of college graduates and 30 percent of those with postgraduate degrees.
Of the Georgia Republican primary voters who want a candidate who has experience in politics (40 percent of voters), 40 percent support Rubio. Of those who are looking for someone outside the political establishment (51 percent), 59 percent support Trump.
This post has been updated to reflect the correct percentage of college graduates Rubio is winning in Georgia.
7:07 p.m.Here's a closer look at the Virginia primary, where Trump and Rubio are fighting for the top slot.
Trump voters are angry at the way the federal government is working, want a temporary ban on non-citizen Muslims, and are very worried about the direction of the economy. Trump runs most strongly among less affluent voters and those with less education.
Sixty-four percent of Republican voters support a temporary ban on Muslims who are not U.S. citizen from entering the U.S. Of those, 44 percent voted for Trump, 24 percent for Rubio and 16 percent for Cruz.
Of the 32 percent of voters who opposed a ban, 49 percent voted for Rubio, 22 percent for Kasich, 11 percent for Trump and 13 percent for Cruz
Rubio benefited from people who made their decision in the last week - 43 percent of his supports said they decided in the last week. On the other hand, 86 percent of Trump supporters had made up their minds earlier than that.
Just 16 percent of primary voters said that someone who could win in November was the most important quality they were looking for but 57 percent of those people voted for Rubio.
As in previous contests this year, support for Trump varies strongly by education.
Forty-seven percent of those with no more than a high school degree voted for him. That drops to 30 percent of those with a college degree and 23 percent of those with post-graduate degrees.
Rubio runs ahead of Trump among those with college degrees (36 percent to 30 percent) and runs far ahead among those with post-graduate degrees (38 percent to 23 percent).
7:00 p.m.CBS News projects that Donald Trump is likely to win the Georgia primary, while Vermont and Virginia remain toss-ups. Trump and Kasich are battling for the lead in Vermont, while Trump and Rubio are competing in Virginia.
6:50 p.m. Here's a reminder about when the polls close in each state voting today:
7 p.m. ET: Georgia, Vermont, Virginia
8 p.m. ET: Alabama, Massachusetts, Oklahoma, Tennessee
8:30 p.m. ET: Arkansas
9 p.m. ET: Texas; Colorado and Minnesota caucuses begin
12 a.m. ET: Alaska caucuses; Wyoming caucuses
6:38 p.m. Dissatisfaction with the federal government runs deep among Virginia Republican voters:
6:26 p.m. A majority of Georgia Republican voters are looking for a president who comes from outside the political world:
6:12 p.m. Here's a look at what Texas voters are looking for in a candidate:
5:25 p.m. CBS News' first exit poll results are in for nine states (Alabama, Arkansas, Georgia, Massachusetts, Oklahoma, Tennessee, Texas, Virginia, and Vermont).
Among Republican voters, the economy and jobs are the most important issue for voters in all states except Oklahoma and Arkansas, while the most important candidate quality for a nominee is that they "share" voters' values.
Large percentages of Republican primary voters are angry at the way the federal government is working and feel that they have been betrayed by Republican politicians.
They are also strongly in favor of temporarily banning Muslims who are not U.S. citizens from entering the country: support ranged from 64 percent in Virginia to 78 percent in Alabama and Arkansas. (Support was 69 percent in Georgia, 72 percent in Tennessee, and 65 percent in Texas).
CBS News' Rebecca Kaplan and Reena Flores and CBS News Poll Analysts Stanley Feldman, Melissa Herrmann and Jeanne Zaino contributed to this report.