Joe Biden was sworn in as the 46th US president at the Capitol in Washington
He signed 15 executive orders in his first action as president - including to rejoin the Paris climate accord
Kamala Harris took her oath as vice-president - the first woman to hold that position
In his first speech, Biden said "this is democracy's day" and that the US "has much to do in this winter of peril, much to repair"
At the inauguration ceremony, Lady Gaga sang the US national anthem, and singers Jennifer Lopez and Garth Brooks performed
Amanda Gorman, 22, became the youngest poet to perform at a presidential inauguration
Donald and Melania Trump left the White House for the last time and flew to Florida
"So with purpose and resolve, we turn to those tasks of our time," says Biden as he concludes his speech on the theme of American unity.
Next up is Garth Brooks singing Amazing Grace.
Image source, Getty Images"What are the common objects that we as Americans love?” asks Biden.
“Opportunity, security, liberty, dignity, respect, honour, and yes, the truth,” he says to applause.
He says the events of the past few weeks - in which President Trump and his supporters have claimed without evidence that Biden’s victory was stolen - have taught us: “There is truth and there are lies. Lies told for power and for profit.”
We must end this "uncivil war" that pits red against blue,” he says, referring to Republicans and Democrats.
"The answer is not to turn inward, distrusting those who don’t look like you or worship the way you do or don’t get their news from the same source as you do."
He asks that those in the audience hold a silent moment of prayer "for those we've left behind and for our country".
He is giving his inauguration address in front of a largely empty Mall that would normally be filled with supporters if not for the raging Covid-19 pandemic.
Anthony Zurcher
BBC North America reporter
Joe Biden knows he has a hard job ahead of him.
In his inaugural address, he has outlined the biggest challenges facing his presidency - a devastating pandemic, massive job losses, a threatened environment, calls for racial justice, and a resurgence in political extremism.
Biden will offer his laundry list of solutions soon enough, but in his first address as president he has offered one overarching prescription: unity.
“Without unity, there is no peace, only bitterness and fury,” he said. “This is our historic moment."
Image source, Getty ImagesThe new US president takes a moment to acknowledge the inauguration of Kamala Harris.
"Here we stand 108 years ago, thousands of protesters tried to block brave women marching for the right to vote.
"Today we mark the swearing in of the first woman in American history elected vice-president - Kamala Harris.
"Don’t tell me things can’t change," he said.
Biden is calling for more mutual respect in society, saying that unity is necessary for American greatness.
"Stop the shouting and lower the temperatures," says Biden, adding that "without unity there is no peace".
"Unity is the path forward," he continues.
"And we must meet this moment as the United States of America," he says, emphasising the word "united".
Image source, Getty Images"The forces that divide us are deep and they are real - but they are not new," says Joe Biden
"The battle is perennial, and victory is never assured.
"Our better angels have always prevailed," says the new president, citing moments from US history such as the Civil War.
"History, faith and reason show the way of unity," he says.
We must meet this moment as the United States of America, he stresses.
Speaking of the challenges that his administration will face, including the pandemic and the rise of "white supremacy", Biden says he will "confront and we will defeat" each obstacle.
He repeats his campaign vow to "restore the soul of the future of America," but says doing so "requires so much more than words".
"It requires the most elusive of all things in a democracy: Unity."
Mark Savage
Music reporter, BBC News
Image source, ReutersBy Lady Gaga's standards, it was a relatively low-key performance in Washington.
There were no dancers, no pyrotechnics and the only outrageous part of her outfit was the outsized golden brooch in the shape of a dove of peace (the colour matched her microphone and earpieces, lest you thought the whole ensemble was just thrown together).
That put the focus on her vocals, which were strong and assured, as she glided through the notoriously wide-ranging melody and its tricky vocal leaps.
Gaga, a vocal critic of the Trump administration, tweeted shortly before the ceremony that she wanted her performance to provide a moment of coming together after the divisions of the last four years.
"Singing our National Anthem for the American People is my honour," she wrote. "I will sing during a ceremony, a transition, a moment of change - between POTUS 45 and 46. For me, this has great meaning.
"My intention is to acknowledge our past, be healing for our present, and passionate for a future where we work together lovingly. I will sing to the hearts of all people who live on this land."
Image source, Getty Images"I thank my predecessors from both parties who are here today," says the new president. Former Presidents Clinton, Bush and Obama are attending the ceremony.
Biden says he spoke to President Jimmy Carter - who is 96 - by phone, and salutes him for his lifetime of service.
His immediate predecessor, Donald Trump, chose not to attend the inauguration.
Image source, Getty Images"We learned again that democracy is precious. Democracy is fragile and at this moment, my friends, democracy has prevailed," Biden says.
"Now, on this hallowed ground, where just a few days ago violence sought to shake the Capitol’s very foundation, we come together as one nation, under God, indivisible, to carry out the peaceful transfer of power as we have for more than two centuries."
He is speaking from the spot that two weeks ago was overrun by a pro-Trump mob as the Capitol was stormed.
Image source, Getty Images"This is America’s day. This is democracy’s day. A day of history and hope.
"Through a crucible for the ages, America has been tested and it has risen to the challenge. Today we celebrate a triumph not of a candidate but of a cause, a cause of democracy"
Image source, Getty Images"This is democracy's day," he says, in his first remarks as US president.
After vowing to uphold and defend the Constitution of the United States, Joe Biden has officially been sworn in as US president.
His oath of office was administered by Supreme Court Justice John Roberts.
Image source, ReutersBiden will be sworn in on a Bible that has been in his family since 1893 and was used during his swearing-in as vice-president in 2009 and 2013, according to CBS News.
The same Bible was also used each time he was sworn in as Delaware senator.
The book itself is five inches (12.5cm) thick with a Celtic cross on the cover.
The family Bible was also used by his late son Beau when he was sworn in as Delaware attorney general in 2013.
Image source, ReutersLady Gaga performed earlier.
Singing with a gold microphone and a large gold dove pinned to her chest, Lady Gaga belted out the US national anthem.
In a high-neck black dress with a prominent red skirt, she sang the anthem to the poignant display of US flags instead of the traditional inauguration audience.
Image source, Getty ImagesThe inauguration of Kamala Harris is historic - no matter your politics.
This is the first time a woman, let alone a black and Asian-American woman, has been inaugurated in one of the two highest positions in the US government.
She follows 48 men who have held the position of vice-president before her.
“While I may be the first woman in this office,” Harris vowed in her victory speech in November, “I will not be the last, because every little girl watching tonight sees that this is a country of possibilities.”
Kamala Harris has just been sworn in as the first female vice-president in US history.
She was sworn into office by Supreme Court Justice Sonia Sotomayor, who made history in 2009 as the first Latina on the top court.
Spotting famous faces in the (significantly smaller than usual) inauguration crowd is a challenge today, given the rigorous safety protocols surrounding the event.
Joe Biden has been resolute and consistent about the need to wear masks to overcome Covid-19.
Later on, after taking his oath, he will sign an executive order requiring masks to be worn on federal property and will also ask all Americans to wear masks in public for 100 days to help combat the virus spread.
Image source, Reuters
Image source, ReutersFather Lee O’Donovan conducts the invocation.
He is well known to the Biden family and presided over the funeral of Joe Biden’s son Beau.
Image source, Getty Images