This is historic: Hillary Clinton is the first woman presumptive nominee of a major party

For the first time in American history, a woman has become a major political party's presumptive nominee for president.

With her victory in New Jersey on Tuesday night, Hillary Clinton officially won a majority of pledged delegates over Vermont Sen. Bernie Sanders. Democratic primary voters have spoken, and they have chosen a woman to lead their presidential ticket in 2016.

"Tonight's victory is not about one person," Clinton said Tuesday night. "It belongs to generations of women and men who struggled and sacrificed and made this moment possible."

It's a historic moment. And for those who think that electing a woman president is a crucial part of advancing women's political representation, it's finally time to start celebrating a major milestone. It's not the White House, but it's the closest a woman has ever come to it in the history of American politics.

Clinton spoke about how on the day her mother was born, Congress was passing the 19th Amendment to the US Constitution that gave women the right to vote. "And I really wish my mother could be here tonight," Clinton said. "I wish she could see what a wonderful mother Chelsea has become and could meet our beautiful granddaughter Charlotte. And, of course, I wish I could see her daughter become the Democratic Party's nominee."

Many observers have long assumed this moment would come. But now this is actually happening.

Clinton's primary victory was never guaranteed

Sanders's campaign has remained formidable throughout the primary season, and Clinton said Tuesday night that he has run an "extraordinary campaign."

Indeed, some Bernie Sanders supporters may argue that Clinton still hasn't mathematically "clinched" the nomination — that it is still technically possible for Sanders to win if enough superdelegates decide to support him at the convention.

This outcome is vanishingly unlikely, since superdelegates tend to follow the will of the voters. And the race has been effectively over for a while, despite protestations of Sanders supporters to the contrary. Clinton made the same argument as Sanders about superdelegates in the 2008 primary, but she faced a much smaller vote gap — and she conceded the race to Obama a few days after the final states voted. Many observers predict that Sanders will do the same sooner rather than later.

Sanders supporters have some legitimate beefs with the way the primary has been covered in the press, particularly the way the media has treated Clinton's nomination as an inevitability. Many Sanders backers were outraged that the Associated Press and NBC News decided to call the race for Clinton on the day before the final primaries.

And Clinton surrogates have been doing some grumbling of their own recently. Some complain that the AP and NBC effectively stole Clinton's thunder and spoiled the big moment that everyone knew was coming Tuesday night, the moment Clinton actually won a majority of pledged delegates and could credibly declare victory.

Others have been frustrated that Sanders has continued campaigning despite his increasingly unlikely odds of winning, which they say is bad for Democratic Party unity and doesn't help Clinton's chances in the general election against Donald Trump. Some have floated the argument that there's a sexist edge to it, with Sanders quixotically carrying on in a way that could actually hurt America's chances of electing a woman president — or, at the very least, spoiling the moment in a certain way.

Not every Democrat and left-leaning voter will celebrate Clinton's victory Tuesday night. But those "18 million cracks in the glass ceiling" that Clinton famously discussed in 2008 have given way to at least one major break. Supporters of Clinton, and those who relish the idea of electing a woman president in general, can feel entitled to take a step back and enjoy the moment.

Actually electing a woman president would be a huge deal — on a practical level as well as a symbolic one

For some who want to see more women in government, a Clinton victory in the general election would be a representational victory in itself. Electing the country's first woman president makes a powerful statement and achieves a major milestone.

But as Vox's Matt Yglesias argued Monday, there's ample political science research to suggest that electing a woman president would also have enormous practical and policy outcomes.

Some research shows that when women are elected to statewide office, it increases female representation in the state legislature by at least 2 percentage points — probably because it helps inspire more women to run for office. That's more than double the 1-point bump you get from a state women's political recruitment campaign.

There's also ample evidence that shows women in office tend to focus more than men on issues that affect women specifically, like child care or reproductive rights — even after taking political party into account.

And if these are the effects we see for more obscure offices like the governorship or legislatures, imagine what electing a president could do.

The bad map we see every presidential election

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