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Here are some of the statements made by Hillary Clinton and Donald Trump in their second presidential debate and how they compare with the facts.

Claim: Donald Trump was quizzed at the start of the debate on his obscene comments about women made in 2005. He went on the offensive with a series of claims - including this one - about women who have alleged sexual assault or obscene behaviour by Bill Clinton.

Reality Check verdict: Bill Clinton did pay out the money to Paula Jones but it was not a fine. In 1999, the then-president reached an out-of-court settlement with Ms Jones, an Arkansas government employee who claimed he had exposed himself to her in a hotel room eight years earlier, when he was governor of Arkansas. He paid Ms Jones $850,000 for agreeing to drop the case but did not offer an apology. Almost half of this sum came from the Clintons' family savings.

Ms Jones had sued Mr Clinton for sexual harassment. It was this case that led to the investigation in which then-President Clinton denied under oath having sex with Monica Lewinsky.

'Mrs Clinton was no longer secretary of state for President Obama's 'red line' in Syria'

Claim: Hillary Clinton had left President Barack Obama's government by the time he drew a "red line in the sand" over the use of chemical weapons by President Bashar al-Assad's forces in Syria.

"First of all, she was there as secretary of state with the so-called line in the sand," said Mr Trump during Sunday's debate. "No I wasn't. I was gone," Mrs Clinton responded.

"At some point, we need to do some fact-checking here," she added. Mr Trump then went on: "You were in total contact with the White House, and perhaps, sadly, Obama probably still listened to you."

Reality Check verdict: Mrs Clinton was secretary of state when Mr Obama made his "red line" comment in August 2012. She stayed in office until February 2013.

In fact, she repeated Mr Obama's comment several times, including at a news conference in Prague in December 2012 when she said: "We have made our views very clear. This is a red line for the United States. I'm not going to telegraph in any specifics what we would do in the event of credible evidence that the Assad regime has resorted to using chemical weapons against his own people, but suffice to say we are certainly planning to take action if that eventuality were to occur."

However, when the "red line" was crossed and more than 1,000 people died in a chemical attack in Damascus in August 2013, Mrs Clinton was no longer the secretary of state. She had been replaced by John Kerry.

Claim: Donald Trump attacks Hillary Clinton over her record on defending women's rights.

Reality Check verdict: It would be a stretch to say Clinton was laughing at the victim. Trump was referring to a case from the mid-1980s, when Mrs Clinton was working as a lawyer. She defended a factory worker accused of raping a 12-year-old girl.

In unpublished audio recordings of an interview she had with an Arkansas reporter, she is heard laughing four times while discussing the trial. In one instance she says: "Of course he [the defendant] claimed he didn't [rape her]…He took a lie detector test. I had him take a polygraph, which he passed, which forever destroyed my faith in polygraphs". Clinton and the reporter are then heard laughing.

The accused ultimately admitted a reduced charge and the victim has since said Clinton put "me through hell".

'Acid-washed emails'

Claim: Donald Trump claims Hillary Clinton "acid washed" 33,000 personal emails to delete them, something he said was an "expensive process".

Reality Check verdict: A claim that has been debunked before. The FBI said Clinton's team used a free software programme called BleachBit. No chemicals were used. When he first made this claim, Trump's campaign said that he did not literally mean "acid washed", adding that it was a play on words and reference to a joke made by Clinton about "wiping" her email server with a cloth. BleachBit debunked Trump's claim on its website saying the software is not "very expensive," adding that it is completely free of charge.

US nukes are 'old' and Russia's are 'new'

Claim: Mr Trump said that the US nuclear programme has fallen way behind that of Russia. The Russians "have gone wild with their nuclear programme" he said, and Russia's nukes are "new" while America's are "old".

Reality Check verdict: Mr Trump has a point.

Even the US Defence Secretary Ash Carter accepted in a speech last month that the US has not built "new types of nuclear weapons or delivery system for some twenty five years". He acknowledged that most of America's nuclear weapons delivery systems "have already been extended decades beyond their original expected service lives".

Meanwhile Russia has been modernising, though not at a pace that might be described as going "wild". Russia's military doctrine certainly places growing emphasis upon nuclear weapons and it is not only modernising its arsenal, but also making nuclear threats against a number of NATO members. Russia's modernisation effort though is constrained by its budget and it still has many older systems deployed too.

The fact is that the world changed at the end of the Cold War. The emphasis moved away from nuclear deterrence and arms control treaties, prompting significant reductions in the two main nuclear powers' arsenals.

Now things have changed again. As Russia gets more assertive, North Korea quickly develops its nuclear programme and China grows its arsenal, the US is seeking to modernise many of its nuclear systems.

Claim: Donald Trump says he has the backing of 200 military leaders.

Reality Check verdict: This seems overblown. The Trump campaign website, in September, said 88 retired US admirals and generals had signed a letter endorsing the Republican candidate. The BBC covered this at the time - you can read the story here.

Canadians are going to America for operations

Claim: Donald Trump says Canada's universal health care system, which he says is similar to the Affordable Care Act, known as Obamacare, leads to longer waits for operations, with Canadians increasingly travelling to the US "when they need a big operation".

Reality Check verdict: There is no readily available data on the number of Canadians travelling to America for medical treatment.

Medical experts also stress that there are several key differences between the US and Canadian healthcare systems, making direct comparisons difficult.

The Trump campaign cited a report by the Fraser Institute think tank, which suggested there was a 25% increase in Canadians travelling abroad for non-emergency medical treatment between 2013 and 2014. The estimate is based on data from an annual survey of Canadian physicians in 12 specialties. This data was combined with figures on the number of procedures performed in Canada to arrive at the estimate.

A 2002 Michigan university study, based on data gathered in three US states bordering Canada between 1994 and 1998, found "surprisingly few" Canadians travelled to the US for treatment.

A 2015 study by the Commonwealth Fund found longer waiting times for specialised care in Canada compared with the United States. But Canada tends to come out slightly ahead of the US in patient-reported measures of physician quality.

Claim: Donald Trump refuses to back down over his claim that he did not support the Iraq War.

Reality Check verdict: It has been debunked. Trump did not publicly speak out against the war before it started. More details from the first debate Reality Check.

Claim: Donald Trump mocks Hillary Clinton for saying she was just quoting from the film Lincoln when she said that politicians should have different positions in public and private. "Abraham Lincoln never lied - that is the big difference between Abraham Lincoln and you," he tells his Democratic rival.

Reality Check verdict: The Clinton quote Trump is referring to - "you need both a public and a private position" - comes from an April 2013 speech to the National Multifamily Housing Council. It was one of the paid speeches she gave before launching her presidential bid, which she refused to release, but details of which have now been revealed in leaked emails.

In the speech, she referred the film Lincoln, and the deal-making that went into passage of the 13th Amendment, a process she compared to sausage-making.

She said: "It is unsavoury, and it always has been that way, but we usually end up where we need to be, but if everybody's watching, you know, all of the back-room discussions and the deals, you know, then people get a little nervous to say the least. So, you need both a public and a private position.''

Reporting by Brian Wheeler, Nalina Eggert and Jonathan Marcus