(CNN) -- Donald Trump and Hillary Clinton came home to New York and both won big.
Trump used his dominating victory as an opportunity to make his case that the only way he'll be denied the Republican nomination is if the game is rigged.
Clinton reveled in her win, which broke Bernie Sanders' string of successes in the West and Midwest.
The victories pushed both candidates much closer to their parties' nominations, leaving their opponents no room for error if either is to be stopped.
Here are five takeaways from New York's primary:
New York's Trump state of mind
New York truly is Trump territory.
The Queens-born businessman put weeks of negative headlines -- from staff changes to delegate losses to abortion flip-flops -- behind him by crushing Ted Cruz and John Kasich in his home state. Exit polls also show New York Republicans believe Trump is the candidate with the best chance to defeat Clinton in the fall.
On stage at Trump Tower, the Republican front-runner surrounded himself with some of his high-profile business friends to cap what he called "an amazing week."
And he set up the Republican contest as one that would have to be taken from him -- unfairly.
"We don't have much of a race anymore, based on what I'm seeing on television," Trump said. "Senator Cruz is just about mathematically eliminated."
Trump, facing a Cruz campaign adept at the inside baseball of delegate-counting, on Tuesday accused the Republican Party of trying to "take the election away" from him. He touted the delegates he would capture in New York, emphasizing he won them in a primary election where voters went to the polls -- an un-subtle dig at Cruz, who has done better in caucuses or party conventions. "The people aren't going to stand for it. It's a crooked system. It's a system that's rigged," Trump told the cheering crowd at Trump Tower.
The good news for Trump shouldn't stop. April 26 -- the next Super Tuesday --- features Maryland, Pennsylvania and other northeastern states that should also be friendly to the front-runner.
Clinton gets the resounding win she wanted
It's a sure sign that Clinton is expecting to celebrate when her campaign announces she'll deliver a speech on the night of a big election.
"This one," Clinton told supporters," is personal."
It's also a win that makes it much harder for Sanders to ever catch Clinton. In a nod to his supporters, whom Clinton would need if she wins the nomination, Clinton said at her victory party: "To all the people who supported Senator Sanders, I believe there is much more that unites us than divides us."
Her commanding victory helped Clinton build on her pledged delegate lead, and it denied Sanders a win that could have changed the dynamics of the Democratic race.
Now, Clinton needs to follow it up with more victories, instead of the speed bumps that have followed big wins in the past, such as Michigan after Super Tuesday.
New York demonstrated once again why Sanders can't seem to catch up. Exit polls showed Clinton performed better than usual among voters ages 30-49 (though Sanders trounced her again with those 18-29), and kept her advantages among minorities, women and older voters. Sanders, meanwhile, still outperformed Clinton with younger voters, men and whites.
Those advantages have been enough for Clinton so far -- and they don't bode well for Sanders in states like New Jersey and California, where he'd need to crush Clinton to have any chance of catching her in pledged delegates.
Bernie sings the blues
Sanders hoped he'd win New York. In fact, as a pro-Clinton group gleefully pointed out Tuesday, he'd said at least 27 times that he expected to win. For two weeks he'd practically moved back to his hometown of Brooklyn.
But Sanders lost big. He congratulated Clinton for her win, but he also was quick to blame the system. New York's primary is closed -- which means only registered Democrats can participate, limiting Sanders' ability to turn out the many independent voters who have helped him win other states.
The closed primary, Sanders said Tuesday evening in Pennsylvania as the crowd booed New York's laws, is "wrong."
"That has got to change in future elections," he said.
Sanders, though, will face the same problem next Tuesday, when Pennsylvania, Maryland, Connecticut, Delaware and Rhode Island vote. Of those five states, only Rhode Island allows independents to vote in the Democratic primary.
Then there were the problems in Brooklyn -- where Clinton has headquartered her campaign, but an area Sanders targeted. There, 126,000 voters were dropped from the registration list since last fall. His supporters were active on social media Tuesday pointing to both the closed primary and the Brooklyn woes as evidence the contest was unfair.
The Sanders camp's eagerness to dismiss New York's results come as tensions flare between the two campaigns. Clinton's aides are furious with Sanders' allegations that she is violating campaign finance rules through her joint fundraising account with the Democratic National Committee -- worried it will do long-term damage to the party's brand and play into Trump's casting of Clinton as "Crooked Hillary." Sanders, meanwhile, unloaded on Clinton over paid speeches, Wall Street contributions and trade in a speech in Pennsylvania.
Still, he hasn't addressed the fundamental weakness of his campaign: an inability to win black voters, CNN political commentator Van Jones notes. He pulled out all the stops in New York, leaning on former NAACP head Ben Jealous, releasing an ad by Spike Lee that featured Harry Belafonte, Rosario Dawson and Danny Glover, and leaning on alliances with the Working Families Party and the Transit Workers Union, both with strong black ties.
If Sanders couldn't improve his performance with African-Americans in New York, it's not clear that he ever will.
Cruz's long night and Kasich's pizza plan
Turns out bashing "New York values" isn't the way to make friends and influence people who vote in the New York primary.
In Philadelphia on Tuesday night, Cruz spoke before New York's polls closed --- sparing him, for the moment, the awkwardness of addressing his third-place finish and his zero delegate haul.
He didn't say anything about the contest at all, aside from noting that it's not surprising for a candidate (in this case, Trump) to win his home state. He'd already campaigned in Maryland on Monday, and is fighting for conservatives in a district-by-district bid to deny Trump delegates.
Everything Cruz did on Tuesday night -- from the location of his event to the 8:30 p.m. ET timing -- reinforced that he wasn't holding his breath for a good night in New York. Aides said if he could hold Trump under 90 of the state's 95 delegates, even that would count as an acceptable result.
Kasich's strategy of eating just about everything in sight -- pizza with a fork at Gino's Pizzeria, soup, a pickle and apple strudel at PJ Bernstein Deli, a massive sub at Mike's Deli -- helped him to a distant second-place finish, but did earn him a few delegates, denying Trump a clean sweep of his home state.
The Ohio governor is hoping the next week's contests allow him to rack up delegates in moderate, suburban congressional districts, using that as a starting point for his argument that he's the Republican best positioned to take on Clinton.
"We're going to be deadlocked" going into the Republican National Convention, Kasich said Tuesday night in Maryland. "Then what delegates are going to do is do something crazy -- consider who can win in the fall."
Democrats enthused; Republicans worried
The Democratic contest has become increasingly heated and personal in recent days -- but even as Sanders amps up the attacks and Clinton's campaign frets over the potential impact, the party's primary voters don't seem worried.
Sixty-seven percent of Democratic voters surveyed in early exit polls said the campaign between Sanders and Clinton has energized the party, while just 29% said it has divided the party.
In the short term, the extended primary is frustrating Clinton's camp. Clinton communications director Jennifer Palmieri called Sanders' campaign "destructive" to the point that Sanders' continuation in the race is "not productive to Democrats" and "not productive for the country."
But in the long run, Democratic voters' engagement and interest in the contest could help Clinton, who will need to consolidate Sanders' supporters if she clinches the nomination -- and could find it easier to do that if they're not turned off by an extended intra-party battle.
Among New York Republicans, it's a different story.
Sixty percent say the GOP campaign has divided the party, compared to 36% who say it has energized it.
That could have something to do with the state's leading candidate, Trump, consistently declaring the nominating process "rigged" against him.
The numbers show that Republicans could have the tougher challenge in bringing the party together behind its eventual nominee.
Trump's Tuesday rout punctuated that reality. His victory made clear that no other Republican stands a chance of catching him at the polls -- even as party members fight to deny him delegates.