TRUMP'S CLAIM: "The children are brought here by coyotes and lots of bad people, cartels, and they're brought here and they used to use them to get into our country." // "They built cages. You know, they used to say I built the cages." // "They are so well taken care of. They are in facilities that are so clean."

FACT CHECK: Trump was defending his now-defunct policy known as "zero tolerance" that required every adult who crossed the border illegally -- even those traveling with their children -- be detained in a bid to deter border crossings.

The result was that thousands of children were separated from their parents in a matter of weeks. It was a major departure from past U.S. policy. In the Barack Obama and George W. Bush administrations, families were separated in rare instances, such as cases of serious crimes like drug trafficking. 

Critics of Trump's policy questioned the conditions the kids were kept in initially at border stations after several died of the flu.

An internal investigation later found that the administration struggled to keep track of the parents, many of whom had been deported. The White House says the parents were contacted and abandoned the children, who were placed with U.S. sponsors, usually family members. The American Civil Liberties Union countered that parents have not been found and contacted and therefore could not give up rights to their children.

Homeland security officials have said that "coyotes" are often used to transport the families for a fee. But there has not been widespread evidence of cases of people falsely presenting themselves as related, with border patrol documenting them as "family units."

Trump's suggestion that "cages" were built by the Obama administration is correct. Obama had faced an influx of children both traveling alone and with families as a result of violence in Central America. And at one point, the Obama administration tried housing the families in special detention centers.

But after a federal judge in California ruled that the arrangement violated a long-standing agreement barring kids from jail-like settings for extended periods, even with their parents, the government began releasing families into the U.S. pending notification of their next court date.

In 2018, photos taken by The Associated Press and posted online by liberal activists suggested the children in steel fencing was Trump's doing. The photos were actually from 2014 when immigration detentions became flooded with families.

-ABC News' Anne Flaherty

TRUMP'S CLAIM: "Joe got $3.5 million from Russia, and it came through Putin because he was very friendly with the former mayor of Moscow, and it was the mayor of Moscow's wife. And you got $3.5 million. Your family got $3.5 million. And, you know, some day you're going to have to explain why did you get $3.5 [million]."

FACT CHECK: In September, Senate Republicans unveiled the findings of their highly controversial investigation into the foreign business dealings of Joe Biden's son, Hunter Biden -- and specifically whether those endeavors ever influenced U.S. foreign policy.

As part of their report, Republicans highlighted an alleged $3.5 million wire transfer sent from Elena Baturina, the billionaire wife of the former mayor of Moscow, to a bank account tied to Rosemont Seneca Thornton LLC, a consultant group that the committee said was co-founded by Hunter Biden.

George Mesires, a lawyer for Hunter Biden, dismissed the claim outright as "false," adding that Hunter Biden "had no interest in and was not a 'co-founder' of Rosemont Seneca Thornton, so the claim that he was paid $3.5 million is false."

Hunter Biden was involved with Rosemont Seneca Partners -- not Rosemont Seneca Thornton, as the Senate Republicans claimed. The two are separate entities, according to Mesires.

Politico reported last month that Trump also sought to engage Baturina's husband, the former Moscow mayor, for business opportunities prior to his time in office.

-ABC News' Luc Bruggeman and Allison Pecorin

BIDEN'S CLAIM: "And to the best of my knowledge, I don't think the president has said anything to Putin about (election meddling). I don't think he's talking to him a lot. I don't think he said a word. I don't know why he hasn't said a word to Putin about it."

FACT CHECK: A smirking Trump, under pressure from members of Congress and his own intelligence community, did in fact tell Russian President Vladimir Putin at the "Group of 20" countries summit last year not to interfere in the 2020 election.

But Trump delivered the warning in a very casual way, playfully wagging his finger at Putin without making eye contact with him, saying, "Don't meddle in the election please, don't meddle in the election."

Trump also pressed Putin in his first G-20 summit meeting on interference in the 2016 election after intelligence officials confirmed Russian involvement in manipulating the election, according to then-Secretary of State Rex Tillerson.

"The president opened the meeting by raising the concerns of the American people regarding Russian interference in 2016 election. Putin denied such involvement, as he has done in the past," Tillerson said at the time.

-ABC News' Matthew Vann

TRUMP'S CLAIM: When asked how he would lead the country during the next phase of the pandemic, Trump said that "there was a spike in Florida, and it's now gone. There was a very big spike in Texas, it's now gone. There was a very big spike in Arizona, it's now gone. And there are some spikes and surges in other places. They will soon be gone."

FACT CHECK: Although cases did "spike" and reach record levels in Florida, Texas and Arizona earlier this summer, then steadily decreased for a few months, cases in all three states have been on the rise for the last several weeks.

Since Oct. 1, the seven-day average of new cases has doubled in Arizona, according to an ABC News analysis of COVID Tracking Project data, recording an average of 880 new cases a day.

In Texas, more than 6,000 cases were reported on Thursday, increasing by 37% in the last two weeks, and in Florida, the seven-day average is still hovering at 3,300 new coronavirus cases a day.

Additionally, nationally, cases are not in fact, going away.

New cases have been rising rapidly for the last five weeks.

Since Sept. 12, the seven-day average of new cases has surged by 77.5%. Just in the last 10 days, the U.S. has reported eight days with over 50,000 new cases reported, and on Thursday, the U.S. reported over 73,000 new coronavirus cases, the highest daily figure in nearly three months.

-ABC News' Arielle Mitropoulos