Exactly what went down in the meeting between Donald Trump and Kim Jong-un today.

US President Donald Trump and North Korean leader Kim Jong-un have pledged to work toward complete denuclearisation of the Korean peninsula while Washington committed to provide security guarantees for its old enemy.

“President Trump committed to provide security guarantees to the DPRK and Chairman Kim Jong-un reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean Peninsula,” said a joint statement issued after their historic summit in Singapore on Tuesday.

DPRK is the Democratic People’s Republic of Korea, the formal name of North Korea.

Trump said he expected the denuclearisation process to start “very, very quickly”.

US Secretary of State Mike Pompeo and North Korean officials would hold follow-up negotiations “at the earliest possible date”, the statement said.

It however did not give any details on how denuclearisation would be achieved. The document also made no mention of the international sanctions that have crippled North Korea’s economy, for pursuing its nuclear weapons program.

Nor was there any reference to finally signing a peace treaty. The combatants of the 1950-53 Korean War are technically still at war, as the conflict, in which millions of people died, was concluded only with a truce.

But the joint statement did say the two sides had agreed to recovering the remains of prisoners of war and those missing in action and repatriating them.

If the joint statement does lead to a lasting detente, it could fundamentally change the security landscape of Northeast Asia, just as former US President Richard Nixon visit to Beijing in 1972 led to the transformation of China.

Before signing what Trump described as a “comprehensive” document, Kim said the two leaders had a historic meeting “and decided to leave the past behind. The world will see a major change.”

Trump said he had formed a “very special bond” with Kim and that relationship with North Korea would be very different.

“People are going to be very impressed and people are going to be very happy and we are going to take care of a very dangerous problem for the world,” Trump said.

Washington to provide unspecified “security guarantees” in exchange for North Korea’s “unwavering commitment to complete denuclearization,” Trump-Kim agreement says https://t.co/3OScA8Njr4

— TIME (@TIME) June 12, 2018

Asked whether he would invite Kim to the White House, Trump said: “Absolutely, I will.”

He called Kim “very smart” and a “very worthy, very hard negotiator.”

“I learned he’s a very talented man. I also learned that he loves his country very much.”

During a post-lunch stroll through the gardens of the Singapore hotel where the summit was held, Trump said the meeting had gone “better than anybody could have expected”.

Kim stood silently alongside, but the North Korean leader had earlier described their summit as a “a good prelude to peace”.

Both men walked to Trump’s bullet-proof limousine, nicknamed “The Beast”, and looked in at the rear seat, with Trump apparently showing Kim something inside. They then resumed their walk.

They had appeared cautious and serious when they first arrived for the summit at the Capella hotel on Singapore’s Sentosa, a resort island with luxury hotels, a casino, man-made beaches and a Universal Studios theme park.

But, with cameras of the world’s press trained on them, they displayed an initial atmosphere of bonhomie as they met on the verandah of the Capella, a refurbished 19th century British regimental officers’ mess.

Body language expert said both men tried to project command as they met, but also displayed signs of nerves.

After a handshake, they were soon smiling and holding each other by the arm, before Trump guided Kim to the library where they held a meeting with only their interpreters.

Inside, they sat alongside each other against a backdrop of North Korean and US flags, with Kim beaming broadly as the US president gave him a thumbs up.

After initial exchanges lasting around 40 minutes, Trump and Kim emerged, walking side-by-side through the colonnaded hotel before entering a meeting room, where they were joined by their most senior officials.

Kim was heard telling Trump through a translator: “I think the entire world is watching this moment. Many people in the world will think of this as a scene from a fantasy…science fiction movie.”

The US dollar jumped to a three-week top on Tuesday and Asian shares rose on the news.

Trump was joined by Pompeo, National Security Adviser John Bolton, and John Kelly, White House Chief of Staff, for the expanded talks, while Kim’s team included former military intelligence chief Kim Yong Chol, foreign minister Ri Yong Ho and Ri Su Yong, vice chairman of the ruling Workers’ Party.

As the two leaders met, Singapore navy vessels, and air force Apache helicopters patrolled, while fighter jets and an Gulfstream 550 early warning aircraft circled.

After the meetings, the two teams and other senior officials met for a working lunch, where beef short ribs, sweet and sour pork and “Daegu Jormin”, or Korean braised cod, were served for the main course, according to the menu.

The North Korean leader’s sister and close confidante Kim Yo Jong was among the lunch party.

As the cameras captured the moment, Trump quipped: “Very nice. Getting a good picture everyone, so we all look nice and handsome and thin…perfect”.

In the hours before the summit began, Trump expressed optimism about prospects for the first-ever meeting of sitting US and North Korean leaders, while Pompeo injected a note of caution whether Kim would prove to be sincere about his willingness to denuclearise.

Pompeo said the summit should set the framework for “the hard work that will follow”, insisting that North Korea had to move toward complete, verifiable and irreversible denuclearisation.

North Korea, however, has shown little appetite for surrendering nuclear weapons it considers vital to the survival of Kim’s dynastic rule.

Sanctions on North Korea would remain in place until that happened, Pompeo said on Monday. “If diplomacy does not move in the right direction … those measures will increase.