7-9 minutes - Source: BBC
The pair held their first campaign event together, a day after Mr Biden unveiled Ms Harris as his number two.
President Trump hit back, saying Ms Harris had "dropped like a rock" in her own presidential bid.
Mr Biden will face Mr Trump, a Republican, in November's election.
What did Biden say?Wednesday's event in Wilmington, Delaware, was not open to the public, with Mr Biden, 77, citing coronavirus prevention needs. Both candidates walked on stage wearing masks to address a socially distanced group of masked journalists.
About 75 people gathered outside in a light rain before the event to catch a glimpse of the two candidates, according to Reuters news agency, although some of the crowd were critics of Mr Biden.
Mr Biden said: "The choice we make this November is going to decide the future of America for a very, very long time."
He continued: "Donald Trump has already started his attacks, calling Kamala, quote, nasty, whining about how she is, quote, mean to his appointees.
"It's not a surprise because whining is what Donald Trump does best, better than any president in American history.
"Is anybody surprised that Donald Trump has a problem with a strong woman, or strong women across the board?"
He also attacked Mr Trump's handling of the coronavirus pandemic, climate change, the unemployment rate and "his politics of racist rhetoric that appeals to division".
What did Harris say?Coming to the podium next, Ms Harris said: "I am ready to get to work."
The 55-year-old former prosecutor told reporters: "This is a moment of real consequence for America. Everything we care about, our economy, our health, our children, the kind of country we live in, it's all on the line."
Ms Harris - the daughter of immigrants from India and Jamaica - continued: "America is crying out for leadership, yet we have a president who cares more about himself than the people who elected him."
She continued: "He [Mr Trump] inherited the longest economic expansion in history from Barack Obama and Joe Biden.
"And then, like everything else he inherited, he ran it straight into the ground."
Ms Harris added: "This is what happens when we elect a guy who just isn't up to the job - our country ends up in tatters, and so does our reputation around the world."
A bare-knuckle fight
Much has been made of the differences between Joe Biden and Kamala Harris since he announced her as his running mate on Tuesday afternoon. Biden is more than 20 years her senior. He's a white man, son of working-class parents in Pennsylvania. She's a multiracial woman from California, daughter of immigrants from Jamaica and India.
In their first joint appearance on Wednesday, however, they both spoke about what they had in common.
"Her story is America's story," Mr Biden said. "Different from mine in many particulars, but also not so different in the essentials."
Ms Harris echoed this, saying that the two candidates are "cut from the same cloth".
It's the kind of message you'd imagine would come from a campaign that's calling for national healing and unity.
Of course, that didn't stop either candidate from going on the attack against their general election opponents.
It's the first salvo for this ticket in what is sure to be a bare-knuckle fight for the White House.
How did Trump respond?At a White House press conference on Wednesday, Mr Trump disparaged Ms Harris' failed bid for the Democratic party's presidential nomination, during which she fiercely attacked Mr Biden's record on race.
Mr Trump said: "I watched her poll numbers go boom, boom, boom, down to almost nothing, and she left angry, she left mad.
"There was nobody more insulting to Biden than she was. She said horrible things about him, including accusations made about him by a woman, where she, I guess, believed the woman.
"Now all of a sudden she's running to be vice-president saying how wonderful he is."
Mr Biden has previously been accused by a number of women of unwelcome contact, including touching and kissing.
Ms Harris told reporters in April 2019 of the allegations: "I believe them." Mr Biden acknowledged at the time that he must respect personal space.
A more serious allegation surfaced this year from a former Senate aide who accused Mr Biden of sexually assaulting her in the halls of Congress in 1993. He denied the claim.
Ms Harris, who had dropped out of the presidential race at that point, said Tara Reade "has a right to tell her story".
Mr Trump has himself been accused by a number of women of sexual assaults, all of which he has denied.
Shortly before the Biden-Harris event, Mr Trump goaded Mr Biden for remaining at home for much of the campaign so far amid the pandemic lockdown.
The president asked a group of teachers at a White House event whether it was healthy for students to be learning in isolation at home.
He then asked: "So if you're a presidential candidate and you're sitting in a basement and you're looking at a computer, that's not a good thing?"
He also tweeted an attack on the Biden-Harris ticket, saying they would put Senator Cory Booker, who is black, in charge of low-income housing in the suburbs. Critics said the tweet was racist.
What happens next?Mr Biden will formally accept the Democratic presidential nomination at next week's party convention, which will largely be a virtual event because of the coronavirus pandemic.
Mr Trump will be nominated for a second four-year term in the White House by his fellow Republicans at their party convention a week later.
A 10-week campaign will follow before voters deliver their verdict in the general election on 3 November.
Mr Trump and Mr Biden are scheduled to hold three debates in Cleveland, Ohio, on 29 September, Miami, Florida, on 15 October, and Nashville, Tennessee, on 22 October.
Ms Harris will hold a debate with Mr Trump's running mate, Vice-President Mike Pence, in Salt Lake City, Utah, on 7 October.