AP Photo, Charles Dharapak
It was held at Hofstra University in New York, and saw the candidates taking questions from the audience on a range of topics.
Here's our point-by-point scorecard of who performed best in each round of the debate:
Round oneQuestion: how would the candidates create more jobs for college graduates?
Romney: Spoke of wanting to make it easier for kids to afford to go to college and of providing more grants and loans. Said "I know what it takes" to create jobs, but didn't say how. Score: 2
Obama: Opened forcefully, talking about his achievements as president, including five millions new jobs in the private sector, and listed specific ways to create more work, including increasing manufacturing and investment. Told the questioner that his "future was bright". Score: 3
Follow-up debate: Romney accused Obama of misrepresenting his remarks over wanting to make "Detroit bankrupt", saying Obama ended up doing the same thing. Obama responded: "Romney doesn't have a five-point plan - it's a one-point plan: the folks at the top play by different rules." Appropriately enough, one extra point each.
Overall score: Obama wins, four points to three
Round twoQuestion: is is the job of the energy department to lower energy prices?
Obama: Discussed his government's energy policy in broad terms, stressing the need to invest in a wide range of energy sources. Promised that within a decade people will be able to travel "twice as far on a gallon of gas". Didn't answer the question directly, and instead argued that all his policies will keep energy prices low. Score: 2
Romney: Attacked Obama's decision to cut the number of permits to drill on federal government lands, at one point accusing Obama of wanting to kill birds. He didn't answer the question either, but said he wanted to get North America "energy indepdent" within eight years and would support more drillings, more permits and licences, and a pipeline in from Canada. Score: 2
Follow-up debate: In a lively exchange of words, Obama repeatedly stated "very little of what Governor Romney said is true". Romney challenged Obama over how many drilling permits and licences he turned down. Obama responded by arguing that companies weren't using licences properly. Romney asked people to compare prices with four years ago, but Obama had a subtle comeback, saying that prices could come down, but only with another recession - which Romney's policies would encourage. He added that his government had built enough pipeline to wrap around the world once. Obama gets extra two points, Romney one.
Overall score: Obama wins, four points to three
Round threeQuestion: by how much would the candidates cut tax credits?
Romney: Talked about wanting to reduce the number of middle-class tax credits but stressed he would not tax middle-class savings. He didn't answer the question specifically. Score: 1
Obama: Defended tax credits as a way to grow the economy, reminding voters of how they helped boost growth during the Clinton years, and argued that wealthy should pay a little bit more. Score: 1
Follow-up debate: Romney stated "I'm not looking to cut taxes for wealthy people," mentioned how reducing tax rates makes it easier for small businesses to keep employees, and boasted "I spent my life in the private sector." Obama made it personal, describing Romney's tax plans as "a sketchy deal" that "doesn't add up." Romney responded that he knew "what it takes to balance a budget. I've done it my whole life." Two points each.
Overall score: a draw, three points each
Round fourQuestion: in what ways do you want to rectify inequalities in the workplace?
Obama: Used the examples of his mother and grandmother working to support his family, and mentioned how the first bill he signed as president was one on equal pay in the workplace. "This is a family issue, a middle class issue," he stressed, and said it would be a key theme of his presidency. Score: 3
Romney: Talked about searching for females to work for him as governor of Massachusetts, and his staff coming back with "bundles full of women". Mentioned that businesses in Romney's America will be "anxious to hire women" but didn't mention any specifics. Score: 1
Follow-up debate: Obama quoted Romney's response to his equal pay act: "I'll get back to you", and broadened the topic to include healthcare, stressing his support of a woman's right to choose on matters of abortion and contraception. Romney responded vaguely, mentioning that he thought "everyone should have contraception". Two more points for Obama.
Overall score: Obama triumphs five points to one
Round fiveQuestion: what is the biggest difference between Mitt Romney and George W Bush?
Romney: "Bush and I are different people, and these are different times," he said. "Our party has been focused on big business for too long... Everything I do is designed to help small businesses grow." He tried to distance himself from his predecessor without criticising him, not entirely successfully. Score: 1
Obama: Used the question to damn Romney by praising George Bush, thereby highlighting what he believed to be Romney's extremism on issues such as drilling for oil and healthcare. Score: 1
Overall score: a draw, one point each
AP Photo, Charlie Neibergall
Round sixQuestion: what would Obama do to earn the vote of those who supported him in 2008?
Obama: Listed all the promises he made in 2008 which he believed he had kept, such as ending the war in Iraq and reforming healthcare. He also listed the things he would like to do if he won a second term, contrasting them with the "promises" of Romney, including cutting taxes for the well-off. Score: 1
Romney: "If you elect Obama you know what you're going to get - we can't afford that," he said, before quoting some of the promises Obama hasn't kept, including cutting the rate of unemployment and cost of health insurance. "He keeps saying I've created five million jobs, but that's after he lost five million," he added, reciting lots of statistics to support his case. Score: 2
Overall score: a narrow win for Romney, two points to one
Round sevenQuestion: how can you help immigrants without a green card living in the US to become productive members of society?
Romney: Said he "welcomed legal immigrants" but wanted the immigration system streamlined, with no amnesty for illegal immigrants and an "employment verification system" introduced. He was hazy on what this would mean in practice. Score: 1
Obama: Also admitted "we need to fix our broken immigration system" but attacked laws that allow some state officials to stop people who sight who "look like immigrants". He referenced his own daughter and attacked Romney for encouraging "self-deportation". Score: 1
Follow-up debate: Romney reminded voters that Obama had promised to fix immigration in his first year in office. He also stressed "We're not going to round-up people... we'll let people make their own choice." The debate went off-topic into a discussion about each candidate's personal investments, with Romney taunting Obama to "look at your pension." Obama responded he didn't need to look, "it's not as big as yours." This got the biggest laugh of the night from the audience. Two extra points for Obama.
Overall score: a clear win for Obama, three points to one
Round eightQuestion: who denied enhanced security for the US embassy in Benghazi and why?
Obama: Talked about US embassy staff around the world. "I know these folks and these families, and nobody is more concerned about these people than me," he said. He warned Romney: "Don't turn national secrity into a political issue," adding "everybody will be held accountable [for the killings in Benghazi] - these are my folks. I'm the one who has to greet these coffins when they come home." Score: 2
Romney: Attacked Obama on the Benghazi killings, asking why weren't the facts clear, and why did president choose the day after the attack to fly to a political fundraiser. He went on to criticise the president's entire Middle East strategy, which is "unravelling before our very eyes." Score: 2
Follow-up debate: Obama was at his strongest here, staring Romney in the eye and accusing him of being "offensive" in choosing to play politics with people's lives. He insisted he did call the attack an "act of terror" the day after it happened, which Romney initially denied, until the debate moderator corrected Romney. Four more points for Obama.
Overall score: a big win for Obama, six points to two
Round nineQuestion: what can be done to increase gun control?
Obama: Stated he believed in a person's right to bear arms, but talked about his experiences of meeting victims of gun attacks. He said he "weapons designed for soldiers in war theatres don't belong on our streets," and would like to introduce a ban on assault weapons. Score: 2
Romney: Said he believed in "no new pieces of legislation on guns" and argued, somewhat oddly, that two-parent families help gun control. Score: 1
Overall score: a close win for Obama, two points to one
Final roundQuestion: how can you bring more jobs back to the US?
Romney: Talked of wanting to make the country a more attractive place for small business and entrepreneurs, and attacked China. "On day one, I'll label China a currency manipulator," he warned. Score: 1
Obama: Agreed with Romney on the need to lower the corporate tax rate, but disagreed on how to do it. Said he supported "trade deals that make sure American workers get a good deal." Score: 1
Follow-up: Romney said "China's been cheating - stealing our intellectual property," while Obama admitted some jobs are never going to come back to the US. Both had weak answers: no extra points here.
Score: a poor draw, one point each
Closing remarksQuestion: what do you believe is the biggest misperception the US people have about you as a candidate?
Romney: Tried to shake-off the legacy of his "47%" remark, saying "I care about 100% of the American people." He also talked about the importance of his faith. "We're all children of the same god," he added. Score: 2
Obama: Attacked Romney for his 47% remark, saying Romney dismissed people who have worked all their lives, students, soldiers fighting overseas and people paying payroll taxes. "I want to fight for them because I believe that if these people succeed, then the country succeeds." Score: 3
Overall score: Obama got the last word: three points to two
Final scoreObama was a changed man from the first debate, appearing confident, alert and passionate. Romney fought hard but was outplayed on a number of key topics.
Obama wins by 33 points to 20.