Kennedy would chide himself afterward for not doing his homework on Khrushchev. Nixon was unsure if he would even meet Mao despite months of quiet planning. And George W. Bush made what in hindsight was a classic first-impression misread of Vladimir V. Putin.

President Trump’s abrupt decision last week to agree to meet North Korean leader Kim Jong-un within two months is a stunning change, after almost seven decades of hostility between two countries that never formally ended the 1950-53 Korean War.

But Mr. Trump will not be the first modern-day American president to come face-to-face with the leader of an adversary, and those encounters have a mixed record. Here are some examples...