With smiles and handshakes and words of mutual warmth, President Trump and North Korea’s Kim Jong Un entered the history books in Singapore on Tuesday as the first sitting leaders of their countries ever to meet face to face. Whether their summit turns out to be a truly historic event depends much more on what comes next.

The United States and the world community have tried before to rein in North Korea. Three recent presidents were parties to agreements in which North Korea pledged to halt its nuclear activity. In each case, the commitments crumbled, the promises proved meaningless, and North Korea continued its steady march toward acquiring nuclear warheads and the means to deliver them across the Pacific Ocean.

Trump and Kim have embarked on a dramatically different approach, eschewing the bottom-up process of the past for a top-down start that the president suddenly and surprisingly agreed to when offered by the North Koreans. But the Singapore summit is only the opening, a first step in what could be lengthy and difficult negotiations between the two nations.

The president is counting on his personal skills to convince Kim that abandoning North Korea’s nuclear weapons program, and the security it provides him, is in his country’s and the world’s best interests. That will require hard bargaining in the future. But the joint communique signed by the two leaders offered scant concrete evidence to back up the North Korean leader’s pledge to “complete denuclearization.”

To reach the goals Trump has outlined will require discipline and commitment that has not been part of the president’s foreign-policy tool kit. And he must resist the kind of impetuousness he displayed on his way to Singapore when he abruptly withdrew U.S. support for a joint communique negotiated with other nations at the Group of Seven meeting in Canada. His pique at Canadian Prime Minister Justin Trudeau’s post-meeting news conference created a rupture in relations with America’s closest allies.

The United States will need the support of countries around the world, especially South Korea, Japan and China to help apply pressure on North Korea to begin the denuclearization process as expeditiously as possible. Yet the summit produced a hiccup with the South Koreans, who appeared caught off guard by the president’s announcement that long-standing, joint military exercises would be halted to lower tensions with North Korea.

Summit meetings are a combination of symbolism and substance. That the president had flown halfway around the world to meet the ruthless dictator of a nuclear-armed nation alone spoke volumes symbolically. That Kim would reverse course after a flurry of provocative missile launches early in Trump’s term to engage in diplomacy also symbolized the change in the climate.

All that freighted with significance the moment of their first greeting. As Trump and Kim greeted each other on a red carpet with the flags of the two nations as their backdrop, the world watched in anticipation. After the earlier insults and incitements, there was no way to overstate the stakes — and worldwide hopes for an easing of tensions — involved in putting Trump and Kim in the same room together, joined only by their translators.

Neither Trump nor Kim appeared stiff or reticent as the two men walked toward each other, arms outstretched for a first handshake. They did not smile for their first formal photograph, but immediately afterward, as they began to walk along a portico, they loosened considerably, and both smiled more broadly. “We will have a terrific relationship,” Trump told reporters after the two men were seated.

That was classic Trump, as was his “very, very good” response to a shouted question from CNN’s Jim Acosta when the two men finished their one-on-one and headed to a bilateral meeting with their advisers. Cameras followed them from one meeting to another, giving the world glimpses of their body language. In a made-for-TV moment, Trump got the kind of public-relations extravaganza he wanted, but without any real hint of the substance of the conversations.

The joint communique that came later did little to answer the questions of what North Korea was prepared to do — and on what timetable — to eliminate its weapons and weapons program. The document stressed the historic nature of the meeting between the two leaders but included few details about the negotiations that lie ahead.

The record from history long ago etched a handful of summits in collective memory: the Yalta Conference of 1945 among Franklin D. Roosevelt, Britain’s Winston Churchill and the Soviet Union’s Joseph Stalin, which shaped the postwar world; the summit in Reykjavik, Iceland, in 1986 between Ronald Reagan and Mikhail Gorbachev, which seemed to end in failure but eventually paved the way for a later arms agreement; the personal diplomacy of Jimmy Carter as he negotiated peace between Israel’s Menachem Begin and Egypt’s Anwar Sadat at Camp David in 1978; the brutal encounter between John F. Kennedy and Nikita Khrushchev in Vienna in 1961 that left the young president shaken and may have emboldened the Soviet leader to put missiles in Cuba.

Whether Singapore will be remembered as the beginning of a success or the start of another dead end with the North Koreans will not be written for months, even years.

Many people have pointed to Richard Nixon’s 1972 trip to China and his meeting with Chinese leader Mao Zedong as a possible parallel to the Trump-Kim summit, with each designed to create a thaw in relations long frozen. But historian Margaret MacMillan, who chronicled that trip in her book “Nixon and Mao: The Week That Changed the World,” noted that Nixon’s journey began with far less uncertainty than surrounds the Trump-Kim summit.

“A lot of the groundwork had been done before he got there, and the goals were more modest,” she said. In that case it was to start on a path toward establishing diplomatic relations, which were not completed until after Nixon left office. “Denuclearization is much, much more difficult than establishing diplomatic relations,” she added.

Historian Robert Dallek, noting parallels and differences between the 1972 Nixon visit and this week’s events, said, “We weren’t going to ask them [the Chinese] to change governments or cut back on developing armaments of any kind.” The Trump administration is not pushing for regime change in North Korea; to the contrary, the president and Secretary of State Mike Pompeo have sought to assure Kim that this is not the goal of these talks.

The risks for both Trump and Kim are significant, although the North Korean leader already has gotten what his predecessors did not, which is a meeting with the president of the United States. But he wants and needs more.

Bill Richardson, who was ambassador to the United Nations during the Clinton administration, said the very fact of the summit was a win for North Korea “because it illustrates the stature of Kim as a world figure and helps him domestically.” But he added that Trump’s decision to accept a meeting “is worth the risk” — if there is an agreement. “Negotiating with North Korea from the bottom to the top doesn’t work,” he added, referring to the approach of previous administrations. “Maybe top-to-bottom will work.”

Trump has said many times he is prepared to walk away from negotiations with North Korea if he concludes that Kim is not serious about denuclearization. But failure is not in the interests of either leader.

Wendy Sherman, a former State Department official with experience negotiating with North Korea and Iran, said the young Kim will want to find a way to stay in power for a long time. But he is under pressure to build the economy of his impoverished nation and open up to the rest of the world without putting his country at risk or himself in jeopardy.

Trump would like to show that he can accomplish what other presidents before him, particularly his immediate predecessor, Barack Obama, have failed to do. He also wants a big foreign-policy success that he could use to help in his campaign for reelection in 2020. “There’s a potential that interests align,” Sherman said. “But it’s still very, very tough.”

The handshakes and smiles set a tone for the day’s meetings and the president was predictably upbeat at the conclusion of the talks. But so much remains to happen. Symbolism is importance, but the substance is everything.