But there's one high-stakes geopolitical riddle that has the potential to do even more to vex the next president of the United States -- and his or her successors for decades: What should the United States do about China?
The increasingly forceful, wealthy and nationalistic rising great power in Asia will pose one of the most significant long-term foreign policy headaches for whoever becomes commander-in-chief on January 20, 2017.
"It's not that ISIS and Iran and Russia aren't problems, but in the long run, the bigger potential challenge is China," said Aaron Friedberg, a former White House national security aide to Vice President Dick Cheney.
But so far, apart from tycoon Donald Trump, a veteran of toe-to-toe business dealings with the Middle Kingdom, none of the major 2016 presidential candidates has put China high on their campaign agenda.
Yet while the more immediate foreign policy challenges facing the United States may provide better political fodder right now, the last candidate standing will eventually have to tackle a problem at least as consequential as Islamic extremism, Greece's potential exit from the euro and Russia's incursion into Ukraine.
"It is almost like they are problems of different intensity burning at a different rate," said Friedberg, now a professor at Princeton University.
"In the grand scheme of things, Russia is a burned out case," he continued. "It's playing a stronger hand than it actually has."
Douglas Paal, a former top U.S. representative to Taiwan said: "The public is more concerned with ISIS and Russia before they get to China. They should be more concerned with China than the other two."
Though China is not in the spotlight, there is a foreign policy debate raging in the early stages of the 2016 campaign, as Republicans blast President Barack Obama and his first-term secretary of state and Democratic frontrunner Hillary Clinton
over their stewardship of U.S. power.
GOP candidates claim Obama's troop withdrawals sparked chaos in Iraq that led to the rise of ISIS. He is accused of showing weakness abroad, of capitulating to Iran in nuclear talks and straining U.S. alliances in the Middle East.
China projects its power
As the debate intensifies, China has not been idle, projecting its own influence in East Asia -- some analysts believe to the detriment of U.S. aspirations to remain a dominant Pacific power.
China has been building up reefs in South China Sea areas also claimed by U.S. allies in a heavy escalation of territorial tensions simmering in the region. One of the artificial islands includes an airstrip, fueling fears Beijing could one day use the outposts to control navigation in sea lanes crucial to the global economy.
Earlier this year, China's Cabinet, The State Council, reoriented the country's naval program to prioritize "open seas" fleets over vessels suitable for coastal waters, a move likely to raise regional tensions even further.
There have also been several alarming close encounters between the United States and Chinese planes and naval vessels, while China has established new air traffic restrictions in the East China Sea that the United States refuses to recognize.
Meanwhile, Chinese hackers are believed to be behind a massive penetration of confidential U.S. government personnel data, which appears to put American government workers at risk of blackmail and expose U.S. spies abroad.
And given the entwined nature of the U.S. and Chinese economies, there are always fears that an apparent slowdown in GDP growth for the communist giant could dampen the American recovery.
Given that that growth is dipping while China's booming stock markets have shown signs of rockiness, there is increasing anxiety abroad that the bubble could burst. Any resulting large-scale loss of wealth in China -- given the importance of its economic engine -- could have consequences for the global economy more far-reaching than those of the Greek crisis.
National security specialists with an eye on the long game appear alarmed at the way China is evolving.
"China is a rising power, we are a status quo power," former CIA acting director Michael Morell told CNN's Erin Burnett in May. "They want more influence. Are we going to move a little bit? Are they going to push? How is that dance going to work out?"
He emphasized, "This is going to be a significant issue for the next president of the United States."
There have been some muted stirrings in the 2016 race of how the debate over China could play out in the campaign and the presidency beyond, and the trend appears to point to a more confrontational American posture toward Beijing.
Though foreign policy rarely decides presidential campaigns, China gets raised because candidates want to look tough, particularly with a country whose emergence has had a significant impact on the U.S. economy.
Candidates often vow to crack down on its alleged cheating on trade and currency issues as they campaign in swing states hit by the flight of blue collar jobs abroad.
Once in office, however, the reality of how the two nations' economies are interconnected tends to render bombastic campaign trail sound bites hollow. Presidents typically seek an accommodation with China.
Trump takes on Beijing
Of the 2016 candidates, only Trump has so far raised questions about the fundamental tone of U.S.-China relations.
"People say, 'Oh, you don't like China,'" Trump said in his announcement speech last month. "No, I love them. But their leaders are much smarter than our leaders, and we can't sustain ourself with that."
He went on to quip: "It's like, take the New England Patriots and Tom Brady and have them play your high school football team. That's the difference between China's leaders and our leaders."
Another top Republican candidate, Jeb Bush, has adopted a more conventional approach to relations with China, warning that a "deep" relationship with Beijing is vital to stopping disagreements tipping out of control.
"It's so easy to create misunderstandings, that we could easily go from being a competitor to ... being challenged in terms of security if we don't stay engaged at every level," Bush said at the Chicago Council on Global Affairs in February.
"It's the most complex -- going forward -- perhaps the most complex, important relationship that the United States has," Bush said, as befits the son of George H.W. Bush, the first U.S. representative in Beijing before the establishment of full diplomatic relations and who later worked as president to ensure that the 1989 crackdown on students in Tiananmen Square did not derail Sino-American relations.
Bush's Florida rival, Sen. Marco Rubio, is also providing the first hints of a tough China policy.
Rubio said in a letter to Obama last month that he was "deeply concerned" about the Chinese government's "recent aggressive actions against the United States and our allies as well as its increasingly repressive posture at home."
"We need to see a change in Chinese behavior or real consequences for China's increasingly egregious actions," Rubio wrote.
Another GOP candidate, Carly Fiorina, said China's hacking was an attempt to make up for its own liabilities.
"I have been doing business in China for decades," Fiorina said in a video first reported by the Huffington Post.
"They are not terribly imaginative. They're not entrepreneurial, they don't innovate. That is why they are stealing our intellectual property," she charged.
But it is another prominent female politician who presents what might be the most intriguing prospect for U.S.-China relations in the next presidency.
Clinton's tussles with China
Clinton has had a complex, sometimes tense relationship with China's leadership, dating from her speech in Beijing at the World Conference on Women in 1995, which angered her hosts over perceived criticisms of their one-child policy and marked her debut as a major world figure.
As Obama's top diplomat, Clinton rejected the notion that Washington wanted to contain China. But she was also an architect of Obama's pivot to Asia strategy, which has been perceived by some inside China as an attempt to encircle the country with U.S. allies.
She also infuriated China's then-Foreign Minister Yang Jiechi at a regional summit in Vietnam in 2010 by backing the position of Southeast Asian nations that territorial disputes should be addressed in a multilateral forum rather than between individual nations, as China prefers.
Clinton also presided over days of tense negotiations with top Chinese officials concerning the fate of blind dissident Chen Guangcheng, who sought refuge in the U.S. embassy in Beijing in 2012.
Her experiences left her stressing the need for cooperation with China but apparently with few illusions about the ultimate shape of the relationship.
"The jury's still out. China has some hard choices to make, and so do we. We should follow a time-tested strategy: Work for the best outcome, but plan for something less," Clinton wrote in her book "Hard Choices."
Statements by Clinton and other presidential candidates are coinciding with a growing debate within the U.S. foreign policy community about the future shape of China-U.S. relations -- ahead of President Xi Jinping's first state visit to Washington in September.
Depending on developments, the next president may have to weigh whether the strategic rationale that has underpinned eight presidencies since Richard Nixon "opened" China in the 1970s needs some adjustment.
Washington's policy has been based on the idea that China's rise is inevitable and that it should be ushered into an international system based on established trading, economic and diplomatic rules.
The goal is to ensure that a clash between a rising power -- China -- and an established one -- the United States -- that has often historically led to open conflict is averted.
But that approach is beginning to be challenged by Beijing's actions, which are shaping the reality the next U.S. president will inherit.
For instance, China appears to be trying to build an alternative economic and security architecture in the region; it recently thwarted Washington's efforts to dissuade some of its closest European allies from joining a Beijing-led Asian Infrastructure Investment Bank.
"I do think we are seeing more and more indications that they are not a status quo power," said Friedberg. "Ten years ago people were saying that they are learning to play by the rules, and it would be crazy of them not to. Pretty clearly they are not."
He concluded, "There is a vision ... of an Asian order that they have which is very different from the existing one."