Smiling and waving, South Korean President Moon Jae-in met Mr Kim at the border before talks begin.
At the summit venue, Mr Kim said that he hoped for frank discussions.
The historic meeting will focus on the North's recent indications it could be willing to give up its nuclear weapons.
In a moment rich with symbolism, Mr Kim and Mr Moon shook hands on both sides of the border in the demilitarised zone.
The South Korean president briefly stepped into the border into North Korea as well - an unexpected moment.