Trump has now won the New Hampshire and South Carolina primaries against a fractured GOP field, while Sens. Ted Cruz and Marco Rubio are battling for second place.
Clinton worked the Las Vegas casinos like her chances at the Democratic nomination depended on them, and notched a victory that stops Sanders' momentum and puts her campaign on solid footing heading into South Carolina.
Trump ran away from the pack in the Republican primary, leaving two other contenders -- Rubio and Cruz -- in a knife fight for second.
Trump has now taken two of the first three GOP contests, and looks dominant enough that other candidates' chances of surpassing him could hinge on whether the five-candidate field quickly narrows.
With 99% of the expected vote in, Trump won with 33%, well ahead of Rubio and Cruz who were virtually tied at 22% -- but Rubio's position immediately looked better when Bush dropped out, leaving Rubio and Ohio Gov. John Kasich as the only candidates in the so-called establishment lane.
Trump, though, wasn't buying that notion, saying he'd heard similar chatter on TV before giving his victory speech.
"They don't understand that as people drop out, I'm going to get a lot of those votes also," he said.
Trump could be on a course to run away with wins in Nevada and on Super Tuesday, particularly across the southern states that vote March 1.
Clinton's Nevada victory halts Sanders' momentum
As the Democratic race moves to South Carolina, where polls have her well ahead, Clinton could have three of the four early-voting states under her belt heading into Super Tuesday.
Her win stems the momentum Sanders had built by eliminating the gap in Iowa and then blowing Clinton out in New Hampshire. It should calm nervous donors and reassure them of Clinton's strategy.
In her victory speech, Clinton repeated a line that has worked well for her over the past two weeks against Sanders: "The truth is, we aren't a single-issue country. We need more than a plan for the big banks; the middle class needs a raise and we need more jobs. We need jobs that pay well and can't be outsourced, jobs that provide dignity and a future."
Sanders' strength among young voters and liberals, and his credibility with Democratic voters, means he's not going away anytime soon -- especially since the last two weeks of March bring a swath of western states he could win.
But Clinton's advantage among "superdelegates" (the Democratic officials who support her, and cast votes at the party's convention), her organizational strength and her advantage with African-American voters and loyal Democrats leaves Sanders a narrow path.
Bush's road ends
Jeb Bush pinned his hopes on South Carolina, pulling out all the stops, with mother, Barbara Bush, and brother, George W. Bush, campaigning on his behalf. It wasn't enough -- not even close. With half the state's results in, Bush was in a distant fourth place.
The reality for Bush was that the man didn't match the moment.
South Carolina Gov. Nikki Haley's decision to endorse Rubio, even after Bush had developed a relationship and courted her heavily, was a psychic blow. It was a blow at the ballot box, too: One-quarter of South Carolina voters identified her endorsement as important, and half of those backed Rubio.
How tough had things gotten for Bush? Consider this as a sign: Jeb Bush's "Right to Rise" super PAC raised more than $100 million in its first six months. In January? It brought in $380,000.
Bush's exit is huge for Marco Rubio and John Kasich. The last of those two standing will need to consolidate all the support that had gone to Bush. It also opens up a massive fundraising network -- which has Kasich's camp giddy
Clock's ticking for Cruz?
Ted Cruz will end up about 10 points below Trump, in a state where evangelicals dominate the GOP electorate. That's not a good sign for the road ahead.
But he came out Saturday night and gave a rousing victory-like speech.
Cruz portrayed himself as the race's only true conservative in a feisty address Saturday night, saying that "we can go with a constitutional conservative and bring back morning in America."
The problem is not just that Trump is winning -- it's the diversity of his support.
Trump beat the establishment candidates among moderates in New Hampshire. Then he went south and beat Cruz among evangelicals in South Carolina.
It raises the question: Other than the senator's home state of Texas on March 1, where can he beat Trump?
With Bush dropping out, Rubio or Kasich -- whoever's the last man standing -- has serious growth potential, likely picking up most of the rest's so-called establishment supporters.
Cruz will need to find places to beat Trump soon: Starting on March 15, states are winner-take-all -- which means a close second to Trump does no good at all.
Where does Bush's support go?
Bush didn't win many votes compared to his peers -- but he was a fundraising machine, and he snatched up a long list of talented Republican operatives and influential supporters.
What Rubio and Kasich will be focused on in the days ahead is where that money and those key backers go.
Rubio proclaimed it a three-way race in his speech Saturday night. But Kasich's cash-strapped campaign is eager to pick up as many of those donors as possible.
The big question is whether Kasich can pick up enough of Bush's backers to put a lid on Rubio -- keeping him from getting much of a bounce from Bush's exit.
Want evidence that Bush's exit freed up big money?
Look at what the last GOP money machine, Mitt Romney, said in a statement Saturday night: "Today, Jeb Bush followed his family's pattern of putting country above himself. His campaign has been about answers to real problems and about policies to strengthen to our country. It has been a campaign conducted in the finest tradition of dignity and integrity and Jeb Bush gave it his all: he can have no regrets. I am proud to call him a friend."
Sanders concedes South Carolina?
Sanders' concession speech was an abbreviated version of his stump speech, where he emphasized economic inequality and the campaign finance system.
He ended it by declaring "on to Super Tuesday," neglecting next Saturday's South Carolina primary.
Clinton has been treating South Carolina and other Southern states as her firewall, especially given her advantage with African-American voters. Clinton has also aggressively tied herself to President Barack Obama, saying she's best poised to build upon his legacy.
And while Sanders has made some inroads with black voters, it is clear he is frustrated.
Comments like those set to air in a BET town hall on Sunday morning -- in which Sanders accuses Clinton
of pandering for African-American votes by aligning herself with Obama, and saying Obama has been wrong on some issues -- could prove damaging.
"Hillary Clinton now is trying to embrace the president as closely as she possibly can. Everything the President does is wonderful. She loves the President, he loves her and all that stuff," Sanders said in an interview with Marc Lamont Hill, which will air on BET at 10 a.m. Sunday, according to excerpts from that interview. "And we know what that's about. That's trying to win support from the African-American community where the President is enormously popular."
For Democrats, an increasingly liberal electorate
Among the entrance poll numbers that help explain how Sanders become a serious threat to Clinton: 70% of Nevada's caucusgoers identified themselves as liberal.
That's up from the even split in 2008 between liberals and those who called themselves moderate or conservatives.
The movement mirrors the results in Iowa and New Hampshire, and make clear that the party's leftward drift is here to stay.
According to entrance polls, 42% of caucusgoers say they want someone more liberal than Obama and 50% said they want someone who will continue his policies -- the mantle Clinton has reached for in recent weeks.
The race is far from over, and Sanders has the cash and support to go a long way. But the next few states are Clinton country. He looks very likely to lose South Carolina, and then several delegate-rich states on Super Tuesday, like Texas, Virginia and Georgia.
Harry Reid's impact in Nevada
Nevada is still Harry Reid's state -- and the Senate Democratic leader, who hasn't endorsed in the race, made one big move that helped Clinton.
Reid called D. Taylor, who heads the parent union of the Culinary Workers Union, which represents 57,000 Las Vegas workers, mostly in casinos. He pushed Taylor for six at-large caucus sites, and to provide transportation to those sites.
The union's big late move, backed by Reid and by Clinton's campaign: Allowing low-wage employees to have paid time off to go to the caucuses at six major casinos on the Las Vegas Strip.
The Culinary Workers Union is a force in Nevada Democratic politics. It opted against endorsing a candidate in 2016's race, but the flexing of local muscles -- by Reid and by the union -- gave Clinton's campaign an important boost.
And she worked to the finish. Clinton found an extra gear in the days before the caucuses, aggressively courting Las Vegas casinos, and taking big and small meetings with just about any group of employees she could find.