When President Obama and Mitt Romney sit down Monday night for the last of their three debates, two things should be immediately evident: there should be no pacing the stage or candidates’ getting into each other’s space, and there should be no veering into arguments over taxes.

This debate is about how America deals with the world — and how it should.

If the moderator, Bob Schieffer of CBS News, has his way, it will be the most substantive of the debates. He has outlined several topics: America’s role in the world, the continuing war in Afghanistan, managing the nuclear crisis with Iran and the resultant tensions with Israel, and how to deal with rise of China.

The most time, Mr. Schieffer has said, will be spent on the Arab uprisings, their aftermath and how the terrorist threat has changed since the attacks on Sept. 11, 2001. No doubt the two candidates will spar again, as they did in the second debate, about whether the Obama administration was ready for the attack in Benghazi, Libya, that killed J. Christopher Stevens, the American ambassador, and three other Americans. Mr. Romney was widely judged to not have had his most effective critique ready, and this time, presumably, he will be out to correct that.

The early line is that this is an opportunity for Mr. Obama to shine, and to repair the damage from the first debate. (He was already telling jokes the other night, at a dinner in New York, about his frequent mention of Osama bin Laden’s demise.)

But we can hope that it is a chance for both candidates to describe, at a level of detail they have not yet done, how they perceive the future of American power in the world. They view American power differently, a subject I try to grapple with at length in a piece in this Sunday’s Review, “The Debatable World.”

But for now, here is a field guide to Monday’s debate.

LIBYA AND BENGHAZI Both candidates will come ready for a fight on this topic, but the question is whether it is the right fight. Mr. Obama already admitted mistakes on “The Daily Show With Jon Stewart” and promised to get to the bottom of them, but the White House has been less than transparent about what kind of warnings filtered up from the intelligence agencies before the attack on the consulate, and whether there was a way that American security forces could have arrived sooner, perhaps in time to save some of the American lives. No doubt the argument will focus on a narrower issue: why the administration stuck so long to its story that this was a protest against a film that turned into something worse, rather than a preplanned attack by insurgents. For Mr. Romney, the task is to show that the Benghazi attack was symptomatic of bigger failings in the Middle East, a road he started down in the last debate, but an argument he never completed.

IRAN With the revelation in The New York Times on Sunday reported by Helene Cooper and Mark Landler that the Obama administration has secretly agreed in principle to direct, bilateral talks after the election, the urgent question for the candidates is this: in a negotiation, what would you be willing to let Iran hold onto in return for a deal that gave the United States and Israel confidence that Tehran could not gain a nuclear weapons capability? It’s a hard question for both men.

Mr. Romney has said he would not allow Iran to have any enrichment capability at all — something it is allowed under the Nuclear Non-Proliferation Treaty as long as it is abiding by the treaty’s rules — a position that would kill any talks. But Mr. Obama does not want to say the obvious: that he is willing to allow Iran to hold onto some face-saving enrichment capability as long as it does not retain its stockpiles of medium-enriched fuel, which can be converted to bomb-grade. Also, look for answers to the question of whether the United States would back up Israel if it decided to conduct a military strike against Iran. Mr. Romney wants to show that Mr. Obama has created “daylight” between the United States and Israel; Mr. Obama wants to demonstrate that while he has Israel’s back, he is trying to protect the country from taking an action he considers unwise, at least at this stage.

CYBERWAR Mr. Obama cannot talk about “Olympic Games,” the covert program that the United States has conducted against Iran, with Israel’s help, using a cyberweapon against another country for the first time in history. But do Mr. Obama and Mr. Romney consider cyberweapons a legitimate tool in America’s arsenal, or too risky, since the United States is the most vulnerable country in the world? We have never heard either candidate answer the question.

AFGHANISTAN There was a time when Mr. Romney declared that America should not be negotiating with the Taliban, but that it should be killing all the Taliban. He stopped saying that after his aides suggested that it sounded like a prescription for endless war. Now both Mr. Romney and Mr. Obama say they think that America should be out of Afghanistan by 2014, the internationally agreed deadline for the withdrawal of forces, though Mr. Romney has the caveat that he wants to hear from his generals first. (The generals thought that Mr. Obama’s insistence on setting a clear deadline for withdrawal was a bad idea — as did Secretary of State Hillary Rodham Clinton and many others.) So what do we want to hear from the candidates?

Lots.

For starters, if it looks as if Kabul could fall back into Taliban hands in a few years, do either of them think the United States should re-intervene? It would be nice to know if Mr. Obama agrees with his vice president, Joseph R. Biden Jr., that all American troops should be out by the end of 2014, since the White House plan calls for an “enduring presence” of 10,000 to 15,000 troops that would back up the weak Afghan security forces and keep an eye on Pakistan’s nuclear arsenal. (The remaining base would also be a place to launch drone strikes into Pakistan and Afghanistan, when necessary.) And for Mr. Romney, if he believes the pullout in Iraq was too hasty, and the pullout in Afghanistan risks making the same mistake, what kind of continuing presence would he have in mind?

THE ARAB UPRISINGS Afghanistan is already in America’s rearview mirror, but the Arab uprisings are not. Mr. Romney says that the rise of Islamic governments is an Obama administration failure. The White House says that if you have free elections in Islamic nations, you cannot be surprised when the Muslim Brotherhood and the harder-line Salafists win control of the government. The question is how to deal with these governments: conditional aid, to ensure American values are respected? Trade restrictions? Gentle persuasion?

This would also be the area to understand when and why each man would advocate future interventions. Mr. Obama joined in the Libya strike, which Mr. Romney thought was a mistake. But Mr. Obama has been hesitant to do much in Syria — a very different kind of conflict — while Mr. Romney says he would arm the rebels with heavy-duty antiaircraft and antitank weapons. Since the light weapons are already going into the wrong hands, how exactly would he find a way to overthrow Syria’s president, Bashar al-Assad?

CHINA Perhaps the most important long-term subject of the debate. Mr. Romney promises a hard line, saying he would declare China as a currency manipulator from Day 1 of his presidency. But he has not said much about Day 2, or Year 2. This is the moment for each candidate to describe how he would counter China’s growing claims in the South China Sea and other disputed territories, how he would handle trade tensions, and how he would manage a world in which the United States, for better or worse, is going to be reliant on Chinese investment in American debt for years to come. And it is the moment for each to give his view of the leadership change under way in China, where three-quarters of the top political posts are about to change hands.