In a carefully choreographed encounter at around 9 a.m., Trump and Kim shared a 12-second handshake in the courtyard of the British-colonial style hotel against a backdrop of American and North Korean flags.
This was followed by a one-on-one meeting, an expanded bilateral meeting and a working lunch.
After their walk, Trump showed off his car - nicknamed 'The Beast' - to Kim, reports The Straits Times.
Kim and Trump will also sign a joint declaration that might put out a framework for additional talks, reports The Washington Post.
Asked how the discussion went, Trump said: "Very, very good."
The summit, which was almost scrapped by a mercurial Trump last month, comes after a flurry of diplomatic activities and barrage of invective and insults traded between the US President and an equally aggressive Kim.