AMNA NAWAZ: For the first time in history, the world's top court, the U.N.'s International Court of Justice, has been tasked with determining what countries are obligated to do to fight climate change.

William Brangham reports on the young people who were instrumental in bringing this issue to The Hague.

WILLIAM BRANGHAM: Twenty-seven-year-old Cynthia Houniuhi lives in Sydney, Australia, more than 1,000 miles from her home in the Solomon Islands.

But she says just being at the beach reminds her of the ocean's importance in her early life.

CYNTHIA HOUNIUHI, Pacific Islands Students Fighting Climate Change: I was in the sea after school.

I had to cross the sea to go to school.

And during lunchtime, we usually fished for our own lunch, so we would catch about maybe one, if we're lucky.

Sometimes, when we're very lucky, we get four.

WILLIAM BRANGHAM: But because of warming waters and rising sea levels, that ocean, which once gave so much to her and millions of other Pacific Islanders, is now threatening to take it all away.

CYNTHIA HOUNIUHI: This feeling, you know, when the sand is slipping between your fingers, that's what it feels like for us, when we're trying to hold onto our languages, our cultural practices, our land, and it's slipping between our fingers like that, because of the adverse effects of climate change.

WILLIAM BRANGHAM: The island nations in the South Pacific are responsible for less than a third of 1 percent of global greenhouse gas emissions, but these low-lying islands are among the world's most vulnerable to the impacts of that pollution.

As the planet warms, extreme weather events like cyclones are becoming more intense here.

Entire villages, like this one on the island nation of Fiji, have been abandoned made unlivable because of rising seas.

In 2019, frustrated by the chasm between global promises of action and any meaningful change, Houniuhi along with other Pacific Islander law students, decided to try and take the industrialized world to court.

SOLOMON YEO, Pacific Islands Students Fighting Climate Change: If we were to go down in the history books the countries that float in the middle of nowhere, let us not go down without a fight.

Even if we can't protect ourselves, and we can protect people around the world who are also going through the same hardship as us.

WILLIAM BRANGHAM: Solomon Yeo is also from the Solomon Islands, and one of Houniuhi's partners.

Their idea was to get the issue of climate change in front of the world's highest court, the United Nations International Court of Justice, or ICJ.

SOLOMON YEO: We said, why don't we take on this initiative?

Let's choose the most ambitious one.

We have governments in the Pacific.

They're open to climate solutions.

Why not pitch it to them?

WILLIAM BRANGHAM: Their pitch convinced the tiny island nation of Vanuatu with just over 300,-00 citizens to take this issue to the U.N. Vanuatu has felt the impacts of climate change head on.

Just last month, two Category 4 cyclones swept through the island, forcing 10 percent of its people to flee to evacuation shelters.

And Vanuatu's diplomatic efforts led to this moment on the floor of the U.N. General Assembly two weeks ago.

MAN: It is so decided.

(CHEERING AND APPLAUSE) WILLIAM BRANGHAM: Passage of a resolution formally asking the ICJ to specify what states' legal obligations are to address climate change and what the consequences should be for those who fail to act.

Michael Gerrard is a law professor at Columbia University.

MICHAEL GERRARD, Columbia University: A decision from the International Court of Justice would be the most definitive, authoritative statement to date about what international law and human rights law have to say about climate change.

WILLIAM BRANGHAM: It's the first time the International Court of Justice will consider climate change.

Vanuatu's Prime Minister Alatoi Ishmael Kalsakau hailed the historic resolution.

ALATOI ISHMAEL KALSAKAU, Prime Minister of Vanuatu: This is not a silver bullet, but it can make an important contribution to climate change, climate action, including by catalyzing much higher ambition under the Paris agreement.

WILLIAM BRANGHAM: An opinion from the international court would not be binding or enforceable.

Still, experts say it will set an important precedent.

MICHAEL GERRARD: They have a strong influence on the decisions of domestic courts, which do issue enforceable opinions.

We have seen several of these domestic courts issue decisions telling their governments that they have to act, and those governments have acted.

WILLIAM BRANGHAM: The measure passed by consensus, meaning none of the U.N.'s 193 member states, including the biggest emitters like China and the U.S., objected to the resolution.

MICHAEL GERRARD: There's much greater public consciousness of the problem.

And the politics of the U.S. have shifted.

Climate change was a winning issue for the Democrats in 2020.

And I think the Biden administration saw that they didn't want to stand in the way.

That made a huge difference in getting the necessary votes.

WILLIAM BRANGHAM: Solomon Yeo now lives in New York and was in the U.N. General Assembly hall to watch the resolution passed.

SOLOMON YEO: My phone is buzzing with messages.

It's like 1:00, 2:00, 3:00 a.m. in the morning in the Pacific, but people are still waking up and sending in messages and saying how grateful they were.

WILLIAM BRANGHAM: Countries will be able to file submissions to the ICJ about how they have been impacted by climate change.

And experts say it is likely to take at least a year for the court to issue its advisory opinion.

Houniuhi says, while there is still a long way to go, the effort is well worth it to protect future generations.

CYNTHIA HOUNIUHI: I can imagine having -- in the future having a conversation with my child and looking at them in the eyes, if they ask, "Did you do your part?"

I want to be able to look into, if I'm lucky, my child's eye and say: "We did try.

We did try."

WILLIAM BRANGHAM: For the "PBS NewsHour," I am William Brangham.