Biden’s running mate, Senator Kamala Harris, who is of Indian and Jamaican descent, will become the first woman vice-president in US history.

Partisan challenges, record levels of voting and a massive spike in mail-in ballots have fuelled the delay, all during a week that saw daily new US Covid-19 infections top 100,000, an all-time high. Particular attention focused on the swing states of Pennsylvania, Michigan, Wisconsin, Arizona, Nevada and Georgia, prompting people from Houston to Hong Kong to Helsinki to learn the names of obscure US voting districts and details of labyrinthine voting procedures.

The streets of New York, Washington, Philadelphia and other cities erupted with cheers and honking vehicles after the calls for Biden by AP, CNN and other news outlets, and while many will breathe a sigh of relief as an outcome is announced, the election process could be far from over.

Shortly after the race was called, messages from world leaders started to pour in.

UK Prime Minister Boris Johnson said that he “looks forward to working closely together on our shared priorities, from climate change to trade and security.”

Canada’s Justin Trudeau sent out a statement emphasizing “shared geography, common interests, deep personal connections, and strong economic ties” and “work to advance peace and inclusion, economic prosperity, and climate action around the world.”

02:30

Celebrations erupt across the US as Biden named winner in presidential election

Celebrations erupt across the US as Biden named winner in presidential election

Leaders in other parts of Europe - German Chancellor Angela Merkel and France’s Emmanuel Macron - congratulated Biden and Harris. 

Even with a projected winner and a new president-elect, vote tabulation in all 50 states and Washington will continue until all results are formally certified around the country.

Additionally, the Trump campaign is trying to mount legal challenges and calling for recounts in several states. Election experts say that those efforts to change the election results are unlikely to succeed.

As expected, Trump indicated that he will not concede, with his campaign issuing a statement on Saturday that “our campaign will start prosecuting our case in court to ensure election laws are fully upheld and the rightful winner is seated”.

Trump was at his Virginia golf course when the calls for Biden came in, but sent a tweet before departing the White House with the claim that he “won the election, by a lot”.

Recounts and audits are normal, and there is little chance the campaign’s lawsuits can alter the results in Trump’s favour, said Martha Kropf, a professor of political science and public policy at the University of North Carolina at Charlotte.

“For most of the places where they are, the number of votes that would be affected by the lawsuits are too small to make a difference,” she said.

Trump and his allies have also said that they want the Supreme Court to decide the election, though it is unclear what exactly they expect the nation’s highest court to be deciding.

“I think it is very difficult to make a legal case against the outcome and then take it to the Supreme Court,” said Thessalia Merivaki, a political scientist at Mississippi State University. “To dispute the outcome of the election, and if the Supreme Court wants to agree to take that case, if there is a legal ground, I think that is very dangerous territory.”

01:19

Giuliani dismisses Biden's win, says lawsuits will be brought

Giuliani dismisses Biden's win, says lawsuits will be brought

“Because that’s what the campaign is signalling - that Trump appointed this conservative justice for a reason, and he’s expecting for them to rule in their favour,” she added, referring to the controversial appointment of Justice Amy Coney Barrett, who took her seat on the court just a week before election day.

Merivaki added that Trump’s repeated and unfounded claims of widespread fraud were “unprecedented”, and said they could have “enormous” implications on Americans’ trust in the nation’s democratic institutions.

Biden will face huge hurdles when he takes office on January 20. It is uncertain whether the elections will give the Democrats control of the Senate; their margin of control in the House of Representatives has thinned; the Supreme Court now has a decisive conservative majority after Trump’s three judicial appointments; and a raucous progressive wing in Biden’s own party is keen to nudge him to the left.

This all comes as the Covid-19 pandemic worsens, the world’s largest economy craters and bickering in Congress frustrates an economic relief package with millions of Americans scared and out of work.

“Biden will come to power with a Democratic Party quite divided on what the election meant,” said Christopher Miller, assistant professor of international history at Tufts University’s Fletcher School of Law and Diplomacy.

“It’s not easy to govern without your party behind you” and facing a reduced majority in the House, Miller added. “You’re in a position where you have to constantly beg members for favours, giving them a lot of influence.”

Biden will also inherit a US-China relationship in tatters, which will be among his most pressing foriegn policy issues when he takes office.

While analysts say they doubt tensions will immediately de-escalate, some expect more bilateral dialogue.

“I would expect many of the Biden’s policies to bear some resemblance to the Trump administration, e.g. wariness of the national security risks of chinese tech, but shrouded in far more diplomatic negotiation,” said Sarah Kreps, a senior foreign policy fellow at Brookings, a Washington-based think tank.

01:15

People celebrate as Joe Biden win US presidential election, according to the Associated Press

People celebrate as Joe Biden win US presidential election, according to the Associated Press

“I don‘t think we can glean that [former president Barack Obama’s] policies will carry over into a Biden administration” because of issues including the extent to which China’s economic and geopolitical strength, she said. “The Chinese treatment of Uygurs brings the human rights policies into sharp relief and Biden cannot easily take a conciliatory approach to China given the pressure he would face on the US political left regarding China’s human rights policies,” she said.

Randall Kroszner, an economics professor at University of Chicago, who served as a governor of the US Federal Reserve System under former president George W Bush, said Biden would likely continue a hard line against Beijing on intellectual property rights. 

01:51

Trump supporters protest Biden’s presidential victory

Trump supporters protest Biden’s presidential victory

“A new president would give an opportunity for a reset, but these concerns about China are shared across both sides of the political aisle,” Kroszner said. “Biden would likely continue to pressure China for reforms that would open markets and provide stronger legal framework for foreign firms operating in China.”

Meanwhile, David Adelman, a partner with the global law firm Reed Smith and former US ambassador to Singapore under the Obama administration, said Biden’s foreign policy experience in the Asia-Pacific region should reassure leaders there. 

The president-elect was a proponent of Washington’s “pivot to Asia” while serving as Obama’s deputy. That policy sought to shore up relations with Singapore and other countries in the region concerned about Beijing’s growing military presence there. 

“The results are a victory for America’s friends and allies in the Indo-Pacific region,” Adelman said. “Biden and his team are well known in Asia and understand the issues facing the region."

Biden is scheduled to formally accept the presidency in a speech delivered from Wilmington, Delaware at 8pm ET.