Here are the key developments:
Joe Biden is the president-elect of the United States after being projected to win the battleground state of Pennsylvania. He is also projected to win the state of Nevada.
There is no projected winner yet in battleground states Georgia,North Carolina or in Alaska, a Republican stronghold.
Former Republican President George W Bush has congratulated the president-elect while some Republicans remain silent on the Democratic victory.
"I ran as a proud Democrat. I will now be an American president," Biden said in a victory speech in his home city as he urged supporters and Trump voters to come together.
Kamala Harris makes history to become the first black woman and South Asian Vice President-elect.
Biden "is rushing to falsely pose as the winner," Trump said in a statement.
Trump's campaign has already filed legal challenges in Arizona, Georgia, Michigan, Nevada and Pennsylvania, and says it will seek a recount in Wisconsin.
A recount is likely in Georgia, Georgia's Secretary of State said. Biden has increased his lead there.
Biden starts day as president-elect by attending church
After attending church in Wilmington, the president-elect visited the graves of family members in the church cemetery.
US First Lady Melania Trump echoes Trump's call to count every 'legal vote'
Former President George W Bush congratulates President-elect Joe Biden, says election outcome 'is clear'
Former President Bush said he spoke to both Joe Biden and Kamala Harris on the phone and offered his warm congratulations.
"Though we have political differences, I know Joe Biden to be a good man, who has won his opportunity to lead and unify our country," Bush said.
He said that President Trump had the right to request recounts and pursue legal challenges but that the "American people can have confidence that this election was fundamentally fair, its integrity will be upheld and its outcome is clear."
Trump's allies stand by him while some Republicans say results unlikely to change
Republican chairwoman Ronna McDaniel tweeted: "The media doesn’t decide who wins elections, voters do. In multiple states the margins are razor thin with counting ongoing, several of which are headed for recounts."
"The media can project an election winner, but they don't get to decide if claims of broken election laws & irregularities are true," tweeted Republican Senator Marco Rubio.
Most Republicans have stayed silent on the outcome of the race, including Senate Majority Leader Mitch McConnell.
Trump has however broken with tradition by refusing to concede the election. There were recounts in several states following Trump's win in 2016 but that did not stop Hillary Clinton from conceding the election or Trump declaring victory.
Some Republicans have congratulated President-elect Joe Biden, with Senator Mitt Romney calling on the party to get behind the new president.
GOP Senator Roy Blunt told ABC that he thought it was too early to declare Biden the President-elect but said he thought a different outcome was "unlikely."
Protesters hold signs as Trump arrives at Virginia golf club on Sunday
'Now more than ever we need to come together as Americans': Maryland Governor Larry Hogan says
"Everyone should want our president to succeed because we need our country to succeed. We have great challenges ahead of us as a country. Now more than ever, we need to come together as Americans," Governor Hogan tweeted.
Massachusetts Governor Charlie Baker, also a Republican, congratulated the President-elect, stating that if there are court battles, they should move quickly.
"If the courts do get involved, they must move quickly to make fact-based, lawful decisions, because the people of this nation - who came out and voted in record numbers - deserve a government that can work collaboratively to fight COVID-19, rebuild our economy and give people hope that there will be a positive path forward," Baker said.
Trump, quoting Newt Gingrich, repeats claim election was stolen
Donald Trump has refused to concede the US presidential election, repeating his claim that the election was "stolen" while retweeting a quote from former US Speaker Newt Gingrich.
Republican Senator Mitt Romney said that Trump had "a relatively relaxed relationship with the truth".
Romney said he would "prefer to see the world watching a more graceful departure but that's just not in the nature of the man."
Most Republicans have remained silent on the election outcome.
Biden team launches transition website with four main priorities
President-elect Joe Biden has launched a transition website with four main priorities that will be addressed "on Day one":
- Responding to the COVID-19 pandemic including new investments in testing
- Getting people back to work and extending COVID crisis unemployment insurance as part of an economic recovery
- Advancing a plan to advance racial equity
- Investing in infrastructure and jobs that tackle the climate crisis
Others on the transition team include Jeff Zients, the former director of the White House National Economic Council, and Michelle Lujan Grisham, the New Mexico governor.
US election is 'moment of significance' for EU partnership, says von der Leyen
In a video statement, European Commission President Ursula von der Leyen said the US and EU were "friends and allies" and said the election was a "moment of significance".
She called the US-EU partnership "unprecedented" and rooted in "common history and shared values of democracy, freedom, rule of law, the respect for human rights, social justice, and an open economy."
Von der Leyen said the EU was ready to "intensify cooperation with a new administration" to address global challenges.
The EU had a complicated relationship with Donald Trump, who supported the Brexit referendum and criticised NATO, calling it "obsolete".
Trump also withdrew from the Paris agreement and said he would leave the World Health Organisation, actions that Biden has said he would reverse.