What are they thinking in Moscow, Beijing and Delhi?

When Americans choose their next president, the contest is always closely watched around the world.

There are countless ways US foreign policy – and the actions of the White House – has an impact on different parts of the globe.

American influence abroad is sure to play a part in the first debate between Joe Biden and Donald Trump on Thursday.

But it’s not just in Ukraine, Israel and Gaza that this election matters.

Eight of the BBC’s foreign correspondents explain why this election rematch is making waves where they are.

By Steve Rosenberg, Russia editor, Moscow

Imagine you’re Vladimir Putin. Who would you prefer in the White House?

The man who’s called you “a killer” and pledged to stand by Ukraine? (that’s Joe Biden).

Or the candidate who has criticised US military assistance to Kyiv and said he’d encourage Russia to do “whatever the hell they want” to any Nato member country that doesn’t meet defence spending guidelines (a certain Donald Trump).

Always keen to surprise, the Kremlin leader has gone on record as saying he’d actually prefer Joe Biden to keep his job because of his “predictability”.

Such a public endorsement, though, should be taken with an extremely large pinch of Russian salt. Moscow is likely to view the election of a Nato-sceptic, Ukraine-sceptic US president as three lemons for Russia on the geo-political fruit machine.

Not that there’s a guaranteed pay-out for Moscow. The Kremlin was left disappointed by the first Trump presidency.

In 2016 one Russian official admitted to me having celebrated Mr Trump’s victory with a cigar and a bottle of champagne. But the champagne went flat. The Russian authorities had expected an improvement in Russia-US relations – that never materialised.

Who’s to say a second Trump presidency wouldn’t leave Moscow feeling similarly underwhelmed.

Whoever wins the race for the White House, the Russian authorities will be watching closely for signs of post-election political instability and polarisation in America and looking for ways to benefit.

By Laura Bicker, China correspondent, Beijing

Both candidates are vying to be tough on Beijing and have similar economic policies to combat China’s rise including raising tariffs on cheap Chinese goods.

But they have very different approaches to dealing with China’s regional influence.

Biden has shored up relationships there, in the hope that a united front sends a clear message to an increasingly assertive Beijing.

But when president, Trump focused less on being a statesman and more on what he saw was the “best deal”. He threatened to remove US troops from South Korea unless Seoul paid Washington more money.

The biggest difference between the two is on Taiwan.

On multiple occasions, Biden has reiterated a pledge to come to the self-governing island’s defence if President Xi makes good on his promise to reunify Taiwan with the mainland, by force if necessary.

But Trump has accused Taiwan of undermining American businesses and he has expressed opposition to a US bill which sent aid there. That led some to question whether he would be willing to come to Taipei’s aid if needed.

When the US votes, China is unlikely to have a favourite in the fight.

In Beijing’s view, an unpredictable Trump could weaken and divide US allies in the region – but he could also create another trade war.

They won’t be too keen on another four years of Biden either. They believe his alliance building has the potential to create a new Cold War.

By Gordon Corera, security correspondent, Kyiv

There is perhaps no foreign country for whom the US election matters more than Ukraine.

Everyone knows US support in the form of money and weapons has been vital in sustaining Ukraine’s war effort. Few believe that Europe could quickly or easily step into any gap.

But here in Kyiv, most people are less focused on the ins and outs of the campaign than you would expect.

That is because, as one person told me, November feels a long way away. There are more pressing concerns as cities come under attack from Russian glide bombs and as Ukrainian forces battle to prevent Russian advances.

They are very aware of what is being said about Ukraine during the campaign. When it comes to Donald Trump, analysts here know he has talked about bringing an end to a war and that there is talk of cutting aid.

While some fear he could force Ukraine into a deal it does not like, experts caution that what will matter is what someone does in office, not what they say during the campaign or in a debate.

And there is an understanding that even a Joe Biden win will not prevent challenges, given how long it took to get the last aid package passed by Congress.

So the stakes for Ukraine are high but it remains only a spectator, and unpredictability is something Ukrainians have long learnt to live with.

By James Landale, diplomatic correspondent, London

Policymakers in the UK tell me they are looking at the US election with some trepidation.

On one level, there is a nervousness about potential decisions that could affect the UK.

Would a President Trump returning to the White House weaken US military support for Ukraine and cosy up to Vladimir Putin?

Would he pick another fight with Europe over the Nato military alliance? Would he spark a trade war with China?

Would a second-term President Biden increase US isolationism and protectionism? Would he be up for the role physically for another four years?

On another level, there is a broader concern. There is a fear in the UK that a close result on November 5, one that is not accepted as legitimate by many American voters, could lead to political violence worse than the storming of the Capitol in January 2021.

A crisis of American democracy may damage US global leadership and encourage autocrats the world over.

All this worries UK politicians in both major parties as they prepare for their own election on 4 July.

Would they at some point have to choose between supporting democratic values and staying close to a traditional ally? Would they have to choose between the US and Europe on some big issue?

Above all, the US election presents the UK with more uncertainty in an increasingly uncertain world.

By Yolande Knell, Middle East correspondent

Both candidates are being closely watched in the knowledge that the White House race will have real consequences.

President Biden strongly backed Israel after the shocking 7 October attacks and has continued to supply the country with weapons even as he has become more critical of the fighting and the high number of Palestinian civilians being killed.

Overall, polls suggest a higher share of Jewish Israelis think Trump would be better for Israel than Biden. Most disapprove of Biden’s handling of the war. And Palestinians widely see him as neglecting their suffering.

Israelis positively recall how Trump formally recognised Jerusalem as their capital and struck new deals to set up diplomatic ties between their country and Arab states.

He supports the war in Gaza but has also urged Israel to “get it over with,” arguing its image is being damaged.

While Palestinians see little hope in a second Biden term, Trump could see them even worse off. The former president has promised, if elected, to cut off all US aid to Palestinians.

In the longer-term, President Biden continues to support a two-state solution – the established international formula for peace – although he has not given a concrete plan for achieving one. Trump has questioned the viability of an independent Palestinian state.

Conventional wisdom has it that Israel’s Prime Minister Benjamin Netanyahu would like to see Trump back in power. However, the former president is said to resent him for acknowledging Biden’s victory in 2020.

By Samira Hussain, Delhi correspondent

In the eyes of the White House, India is in a sweet spot.

The United States sees India as a geopolitical counterweight to China. India also has the fifth largest economy in the world, set to become the third largest by 2030. Earlier this month, the country held the world’s largest democratic elections which saw Narendra Modi become prime minister for a third consecutive term.

Although India has been accused of democratic backsliding and misrepresenting the true economic picture domestically, none of that really factors for the United States given India’s strategic importance.

Whatever happens in November doesn’t make a difference to how India will operate on the global stage. Both candidates are known entities.

If Biden remains president then the status quo prevails, which means a healthy trading relationship and the red carpet treatment. Just last year Modi was in Washington for an official state visit complete with a lavish reception at the White House in honour of the prime minister who also addressed a joint session of Congress.

If Trump is re-elected, the only difference might be a question of tone. He has previously called Modi an exceptional leader. Trump visited India in 2020 where tens of thousands of people came to see the American president, side by side with their prime minister in Modi’s home state of Gujarat.

Proof that India can deal with whichever political outcome.

By Will Grant, Mexico correspondent

Mexicans have recently held their presidential election making a historic choice: electing Claudia Sheinbaum as the country’s first female president.

Her close ally, outgoing President Andres Manuel Lopez Obrador, forged an unlikely partnership with Donald Trump when he was in the White House. While Mexico’s relations with Mr Biden have at times been tense, the neighbours have consistently found common ground in critical areas like immigration and cross-border trade.

Once in power, Sheinbaum will need to show she is not just an extension of the previous administration – and what better way to do that than through relations with Washington? As such, she may try to be different in tone and approach to her predecessor, if not in substance, when it comes to working with either Biden or a potential second Trump presidency.

Speaking to the BBC on the campaign trail, Claudia Sheinbaum said she was unphased by the prospect of either man in the White House. “I will fight for Mexicans,” she told me.

Mexicans themselves, however, remember Trump’s presidency with no fondness. The provocative rhetoric alone – “drug dealers, criminals, rapists”, as he called Mexican immigrants when he descended the infamous gold escalator to launch his campaign in 2016 – still sticks in the craw for many here.

By Jessica Murphy, BBC News, Toronto

America’s northern neighbour has some worries about a second Donald Trump presidency.

Trump has never been as popular in Canada as with parts of the US public. One poll earlier this year suggested a majority worried that American democracy would not survive another four years of Trump.

Still, while Trump’s time as president put a strain on the bilateral relationship, Canada came away with some wins, notably a successfully renegotiated North American trade deal.

With November’s US election fast approaching, Canada’s political and business class is already ramping up for more trade upheaval.

It’s hard to overstate how closely linked the two countries are, especially economically – about C$3.6 billion ($2.6bn; £2.1bn) in trade crossed the border each day last year.

So a planned formal review of the trade deal, along with Trump campaign musings about a worldwide tariff on imported goods have both been cause for concern.

Prime Minister Justin Trudeau has launched a “Team Canada” project, sending politicians, envoys and business leaders fanning out across the US to pitch the value of Canada, both privately and publicly.

A similar initiative proved successful during the first Trump presidency.

The country will “be ready to deal with whatever gets tossed at us”, Trudeau has said.