HONG KONG — Mike Pompeo, the C.I.A. director and nominee to be the next secretary of state, traveled to North Korea and met with its leader, Kim Jong-un, the strongest indicator to date that plans for direct talks between Mr. Kim and President Trump are moving ahead.

If talks between Mr. Trump and Mr. Kim do happen, they would be the highest-level meeting between the two countries. No sitting president has ever met — or even spoken on the phone — with a North Korean leader.

Here’s a look at previous attempts at dialogue and how the possible summit meeting between Mr. Trump and Mr. Kim came about.