12:33 a.m. CBS news estimates Hillary Clinton will win South Dakota primary.
12:11 a.m. Hillary Clinton appears likely to win California's Democratic primary, according to CBS News reports.
11:28 p.m. CBS News projects that Donald Trump wins the GOP primary in California.
10:56 p.m. CBS News projects that Hillary Clinton wins the Democratic primary in New Mexico. At 2,335 delegates, Clinton has secured the majority of pledged delegates in the primaries.
After his wife secured the majority of pledged delegates, former President Bill Clinton tweeted his own congratulations:
10:35 p.m. CBS News projects that Donald Trump wins the GOP primary in Montana.
10:16 p.m. Presumptive Democratic nominee Hillary Clinton, the first woman to top a major party's presidential ticket, addressed supporters in Brooklyn late Tuesday night, thanking voters and declaring that America has "reached a milestone."
"Tonight's victory is not about one person," Clinton said. "It belongs to women and men who struggled and sacrificed who made this moment possible."
She praised rival Bernie Sanders for engaging in a "vigorous debate" that has been"very good for the Democratic party and for America."
In a pivot to her general election rival Donald Trump, Clinton attacked the billionaire for the inflammatory remarks he has made throughout the Republican primary season, saying "he has abused his primary opponents and their families, attacked the press for asking tough questions, denigrated Muslim immigrants."
Clinton's closing statements emphasized the night's historic moment.
"What I care about most is the history our country has yet to write," she told a cheering crowd. "Our children and grandchildren will look back at this time...We need to make sure that they can be proud of us."
9:47 p.m. CBS News projects that Bernie Sanders has won the North Dakota Democratic caucus.
9:36 p.m. Clinton has a new Twitter avatar.
9:18 p.m. CBS News projects Trump has won New Mexico. Trump has been speaking at his golf course in Briarcliff Manor, New York.
He said that victory "is not a testament to me."
"This is a testament to all of the people who believed real change - not Obama change - but real change is possible," Trump said.
"You've given me the honor to lead the republican party to victory this fall...I understand the responsibility of carrying the mantle and I will never let you down," Trump said. "I will make you proud of your party and our movement."
To Bernie Sanders supporters: "We welcome you with open arms."
Trump also previewed a speech he said he would make "on probably Monday of next week" regarding the Clintons, slamming them for turning "the politics of personal enrichment into an art form for themselves."
"They've made hundreds of millions of dollars selling access, selling favors, selling government contracts, and I mean hundreds of millions of dollars," he said. "Secretary Clinton even did all the work on a totally illegal private server... how she's getting away with this, folks, nobody understands."
Trump added that his speech would be "very informative and very, very interesting."
- June 7 primary races: Where to find all the results https://www.cbsnews.com/news/june-7-primary-races-where-to-find-all-the-results/
- Elections Center (Homepage): https://www.cbsnews.com/elections/2016/primaries/
9:10 p.m. Ahead of Clinton's primary night speech, the Democratic presidential contender tweeted this:
9:07 p.m. CBS News projects Trump has won South Dakota.
9:03 p.m. CBS News projects Hillary Clinton has won New Jersey. Polls have just closed in New Mexico, Montana and South Dakota. North Dakota is caucusing right now.
8:55 p.m. CBS News: Hillary Clinton is leading in New Jersey and appears headed for a win.
8:30 p.m. CBS News projects Donald Trump has won New Jersey.
7:30 p.m. Bernie Sanders isn't out for the count yet.
For days, the Vermont senator's campaign has said Sanders would venture home to Burlington after Tuesday's primary to reflect and recharge.
But on Tuesday, top Sanders campaign aides told CBS News' Nancy Cordes and Kylie Atwood that the Vermont senator plans to head to Washington, D.C. later this week for a "Thursday night rally" and "some meetings." Plane logistics, however, are still being worked out, the campaign says.
Details of the rally and meetings have yet to be announced.
6:30 p.m. Voters in California, Montana, New Jersey, New Mexico, and South Dakota are casting their ballots in their states' Democratic and Republican primaries today. Residents in North Dakota are participating in the Democratic caucuses.
Hillary Clinton and Bernie Sanders are the prominent candidates on the Democratic ballot. Donald Trump is the presumptive GOP nominee, while Clinton locked down the Democratic nomination late Monday.
Stay tuned for CBS News' latest updates.