The view from countries where Trump's win really matters
BBCNews of Donald Trump's return to power in the White House has made global headlines.
His so-called America First foreign policy could see a withdrawal of US involvement in areas of conflict around the world.
Five BBC correspondents assess the effect it could have where they are.
Trump seen as respite on Ukraine frontlines
By James Waterhouse, Ukraine correspondent, Kyiv
"Do not try to predict Trump's actions. No one knows how he is going to act."
The words of one Ukrainian MP reflect the political challenge facing Kyiv. A Trump victory was widely feared here, over what it could mean for future US support.
The Republican once vowed to end the war in a single day, and has repeatedly criticised US military aid for Ukraine. Now, it's anyone's guess what he could do.
"He could ask Putin to freeze this war, and he says 'OK'," says a front-line soldier. "It's the worst scenario because in a couple of years the Russians will advance again and might destroy us."
"The second scenario is if Putin refuses," he says. "There is a chance Trump will react radically. That is a more promising scenario."
Ukraine hopes that means the US further upping its military support in the face of a likely Ukrainian defeat.
For those close to the front lines who have had enough of Russian aggression, Trump is seen as a route to respite.
Volodymyr Zelensky, Ukraine's president once labelled by Trump as "the greatest salesman in history" sent an early message of congratulations.
He talked up the political and economic opportunities a partnership could provide, and wants to be able to keep fighting in return.
There's also another ingredient.
Trump won't just have to consider further military support for Ukraine, but also how or whether to respond to North Korea's growing involvement in Russia's invasion.
No plans for Putin congratulations
By Steve Rosenberg, Russia editor, Sochi
You might expect the Kremlin to be cock-a-hoop at Trump winning back the White House.
After all, out on the campaign trail, he had avoided criticising Vladimir Putin. Kamala Harris meanwhile called the Russian president "a murderous dictator".
Trump had also questioned the scale of US military assistance to Kyiv.
Publicly, though, the Kremlin is going out of its way to give the impression that it's not excited by a Trump victory.
"I'm not aware of any plans [for President Putin] to congratulate Trump," said Kremlin spokesman Dmitry Peskov. "Don't forget that [America] is an 'unfriendly country' which is directly and indirectly involved in a war against our state."
The dampening down of expectations are the result of how Trump's first term turned out: the Kremlin had high hopes that a Trump presidency would transform US-Russian relations. It didn't.
Nevertheless, at the political discussion club I'm attending in the mountains above Sochi, leading Russian political scientists seem to be looking forward to Trump the sequel.
One pundit told me he thinks that under Trump the US will "retreat" from its global super power status.
Another suggested the US election fitted the Kremlin's "overall vision of the world", in which "liberal globalism has depleted its efficiency".
Europe's leaders see security trouble ahead
By Paul Kirby, Europe digital editor
When dozens of European leaders from the EU and beyond gather in Budapest on Thursday, those on the right will be celebrating Donald Trump's election victory, but the rest will be asking themselves what happens next.
Hungarian host and Trump ally Viktor Orban was first on to Facebook with his delighted message: "It's in the bag!"
But for many other EU leaders Trump 2.0 could signal trouble ahead on security, trade and climate change.
Within minutes of congratulating the Republican candidate, France's Emmanuel Macron said he had agreed with German Chancellor Olaf Scholz to work towards a "more united, stronger, more sovereign Europe in this new context".
German Foreign Minister Annalena Baerbock gave an idea of that context. Just back from Ukraine, she said Europeans now had to "think big and make investments in our European security big", with the US as a partner.
Her Polish and Nato counterpart Radoslaw Sikorski said he had been in touch with Trump's top team and agreed "Europe must urgently take greater responsibility for its security".
The prospect of steep US tariffs on EU imports weigh heavily too. EU Commission chief Ursula von der Leyen congratulated Trump but gave a timely reminder that "millions of jobs and billions in trade" relied on their transatlantic relationship.
Israel 'clear-sighted' about who Trump is
By Lucy Williamson, Middle East correspondent, Jerusalem
Benjamin Netanyahu, Israel's prime minister, was one of the first to congratulate Trump and has previously called him Israel's best ever friend in the White House.
Trump previously won favour here by scrapping a US nuclear deal with Iran that Israel opposed. He also upended decades of US policy by recognising Jerusalem as Israel's capital.
Trump's first term in office was "exemplary" as far as Israel is concerned, says Michael Oren, a former Israeli ambassador to the US. But he adds: "We have to be very clear-sighted about who Donald Trump is and what he stands for."
The former president sees wars as expensive, Mr Oren notes, and Trump has urged Israel to finish the war in Gaza quickly.
"If Donald Trump comes into office in January and says, 'okay, you have a week to finish this war', Netanyahu is going to have to respect that."
In Gaza, where the Israeli military has been battling Palestinian group Hamas, desperation has narrowed the focus of some residents.
Trump "has some strong promises", says Ahmed, whose wife and son were both killed when their house was destroyed. "We hope he can help, and bring peace."
Another displaced resident, Mamdouh, said he didn’t care who won the US election - he just wanted someone to help.
Xi might see opportunity on world stage
By Laura Bicker, China correspondent, Beijing
China is bracing itself for the return of Donald Trump where there are fears that his presidency will trigger a new trade war.
As president, Trump imposed tariffs on over $300 billion of Chinese imports. This time around he has said the tariffs could be in excess of 60%.
Beijing will not stand by - it will retaliate. But China's economy is already ailing and it will be in no mood for a second protracted trade war.
Trump's unpredictable policies and fiery rhetoric are also a headache for Chinese leaders who prefer stability.
But in the battle for power and influence, some analysts see an opportunity for Beijing.
The Biden administration has spent the last four years building friendships across Asia with the likes of South Korea, Japan, the Philippines and Vietnam - all in an effort to contain China.
Trump's "America first" doctrine has, in the past, isolated and weakened these US alliances. He prefers trying to make deals over delicate diplomacy and often puts a price tag on America’s friendships.
In 2018, he demanded more money from South Korea to continue to host US troops in the country
Make no mistake, China wants to challenge the US-led world order. Beijing has already built alliances with emerging economies across the so-called Global South.
If Washington's influence does wane in Asia and around the world, it could be a win for President Xi.
North America correspondent Anthony Zurcher makes sense of the race for the White House in his twice-weekly US Election Unspun newsletter. Readers in the UK can sign up here. Those outside the UK can sign up here.