In pictures: Donald Trump and Kim Jong Un in first meeting
The two shook hands firmly before sitting down to talk at a resort hotel in Singapore.
Donald Trump and Kim Jong Un met on a red carpet, dozens of cameras recording their every move, as the world watched the first meeting of a sitting US president and North Korean leader.
Thirteen seconds. That is how long the American and North Korean leaders shook hands at the start of their summit in Singapore.
Smiling, Mr Trump grasped Mr Kim's right arm as they shook hands, and then, later, took ahold of Mr Kim's left arm as they turned to face the cameras and the world. The backdrop was a row of the two nations' flags displayed side-by-side.
Mr Trump predicted that he and Mr Kim would have "a terrific relationship" as they met face to face for the first time.
After the one-on-one meeting, joined only by interpreters, Mr Trump said he was feeling "really great". "We're going to have a great discussion and a terrific relationship," he added.
As he and Mr Kim walked together along a balcony to a larger meeting with aides, the president described the meeting as "very, very good", saying that the two have an "excellent relationship".
Among those joining the leaders on the US side were Secretary of State Mike Pompeo, White House chief of staff John Kelly and national security adviser John Bolton. The North Korean delegation included Kim Yong Chol, a top aide to Mr Kim who recently met Mr Trump at the White House.
At a train station in Seoul, the South Korean capital, people cheered and applauded as television screens broadcast the Trump-Kim handshake live.
The leaders concluded the summit by signing a joint document in which they committed to working towards the "complete denuclearisation of the Korean Peninsula".