In July 1971, during a routine visit to Pakistan, National Security Adviser Henry Kissinger feigned illness and retired to his hotel room to recover. In reality, though, Kissinger was springing into action. Smuggled under darkness from his hotel to the Islamabad airport, he traveled secretly to Beijing, where he held meetings with China’s supreme leader Mao Zedong. A few days after Kissinger’s return, President Richard Nixon announced that he’d be the first-ever American president to visit China. He and Mao held their first summit only seven months later, in February 1972, in a visit that changed the world.

It’s difficult to recapture the shock Nixon’s visit caused at the time. Ever since Mao had taken power in 1949, the People’s Republic of China and the United States had been sworn enemies. Their governments refused to recognize one another, their leaders routinely traded public insults, and their armies fought during the Korean War. As a young congressman, Nixon himself had attacked President Harry Truman with cries of “Who Lost China?” Washington protected the breakaway, non-communist island of Taiwan from invasion and recognized Taipei, not Beijing, as the legally sovereign capital of China. Mao openly speculated about winning a nuclear war because China’s enormous population meant it could absorb more losses than the United States. Yet despite all that, Nixon went to China.

Over the past few months of breakneck diplomacy between Donald Trump and Kim Jong Un, it’s difficult not to hear echoes of Nixon and Mao. Just like Nixon trusted only Kissinger, Trump seems to be relying exclusively on Secretary of State Mike Pompeo for advice on Korea. Pompeo even made his own secret trip to Pyongyang, after which Trump stunned the world with hints of a possible summit with Kim. The main difference with Nixon’s opening to China is thoroughly Trumpian: everything now is unfolding at warp speed.

Nixon and Trump aren’t the only Republican presidents to have embarked on risky summit diplomacy with America’s most bitter enemies. During the Cold War, Republicans frequently held summit meetings with communist dictators (four times with Chinese premiers and a remarkable twenty times with leaders of the Kremlin). By contrast, Democratic presidents rarely met with leaders from Moscow and Beijing (three times with the Soviets and only once with the Chinese), probably because they were terrified of looking soft on national security.

The record of presidential summit diplomacy is mixed, however, and provides little guidance for the historic meeting in Singapore. There simply isn’t a reliable playbook to follow. Personal chemistry and the alignment of interests are both essential for success; but even then, there’s no way to predict the long-term consequences.

In 1959, Dwight D. Eisenhower hosted Soviet Premier Nikita Khrushchev at Camp David. Both were wary. They tried to engage each other by watching Westerns in the presidential movie theater, going to the bowling alley, and visiting Eisenhower’s farm in nearby Gettysburg. However, while cordial, neither leader warmed to the other. They met again in Paris a year later, this time with the leaders of Britain and France, but Soviet air defenses shot down an American U-2 spy plane that had been doing reconnaissance in Soviet air space. Eisenhower refused to apologize, Khrushchev stormed out, and the Cold War entered its most dangerous phase culminating in the Bay of Pigs, the Berlin Wall, and the Cuban Missile Crisis under Eisenhower’s successor, John F. Kennedy.

In 1985, with Cold War tensions at their highest since the early 1960s, Ronald Reagan and Mikhail Gorbachev met in the neutral venue of Geneva. The summit produced little in the way of substance, and the two sides even exchanged in ritualistic recriminations. But Reagan and Gorbachev found they enjoyed each other’s company, and their meeting in Geneva set the stage for a remarkable summit the next year, in Reykjavik, where they nearly agreed to a comprehensive arms-control agreement that would have virtually eliminated their nuclear arsenals. They met yet again in 1987, this time in Washington, to sign the Intermediate Range Nuclear Forces Treaty, a milestone that marked the beginning of the end of the Cold War.

Which example will the Trump-Kim summit follow? Eisenhower’s meeting with Khrushchev sent superpower relations into a tailspin, and when the Soviet leader met Kennedy a year later, their meeting was hostile. “He just beat hell out of me,” JFK said privately. There’s a good chance that “Little Rocket Man” (as Trump calls Kim) and the “mentally deranged U.S. dotard” (Kim’s rejoinder) will do likewise after realizing they don’t have many shared interests after all, and that the Korean peninsula will give the 21st century its versions of the Berlin and Cuban crises.

Nixon’s summit with Mao went much better, partly because the United States and China had shared interests—not least a common enemy in the Soviet Union—and partly because Nixon and Kissinger meticulously planned for it for over a year. Above all, Nixon was committed to forging a new world order in partnership with Beijing. As he explained, “we simply cannot afford to leave China forever outside the family of nations, there to nurture its fantasies, cherish its hates and threaten its neighbors.” Yet Nixon’s strategic pivot brought long-term gains to China with less tangible benefits to the United States. The thaw in U.S.-Chinese relations helped pave the way for globalization, which has been a mixed blessing for the United States but has created the conditions for China’s spectacular ascendance. Even in the short-term, Nixon didn’t achieve his most important goal: to get Beijing’s help pressuring North Vietnam into peace.

The Trump-Kim summit may well end in ambiguity: momentous not for the nuts-and-bolts agreements it produces but simply for the idea that it happened at all. In envisioning an economic jump-start for North Korea, Trump sounds as if he’s keen to bring North Korea back into the family of nations. If he can pull this off, it would be a monumental achievement of world-historical significance. Yet while everyone in the region will appreciate the new era of peace and stability, South Korea and Japan will be wary of a newly dynamic North that could one day be just as assertive as it is today but with much more economic strength behind it. Anyone who underestimates North Korea because of its dilapidated, impoverished condition should remember that China was in much worse shape in the early 1970s, having suffered tens of millions dead from the disastrous centralized industrial planning of the Great Leap Forward and the violent internal divisions from the Cultural Revolution.

For Trump, the best possible outcome would emulate Reagan’s diplomacy with Gorbachev, which resulted in the end of the Cold War almost entirely on American terms and the sudden collapse of the Soviet Union itself. Reagan didn’t expect this to happen, but his summitry helped pave the way; and with his promises of massive economic aid in exchange for denuclearization, Trump may be hoping for a similar result. But Kim is a close student of history, and he will surely avoid rushing into a program of reform that spirals out of control and leads to the end of his family’s regime. The Chinese knew their history too, which is why they kept a tight grip on political power even while liberalizing their economy, thus avoiding what they saw as Gorbachev’s mistakes.

The stakes in Singapore are high. Trump will want to match Reagan’s record, while Kim will hope to emulate Mao. The rest of us better hope that Trump and Kim don’t instead repeat Eisenhower’s acrimonious summit with Khrushchev, once again risking conflict between two nuclear powers. With events moving so quickly, anything could happen.