What was the tense confrontation between Kennedy and Khrushchev that nearly led to nuclear war in October 1962?

That was The Cuban Missile Crisis. The United States discovered nuclear missiles in Cuba. During that time, tension rise to the top. Kennedy ordered low-level reconnaissance missions once every two hours but tensions finally began to ease on October 28 when Khrushchev announced that he would dismantle the installations and return the missiles to the Soviet Union, expressing his trust that the United States would not invade Cuba. Further negotiations were held to implement the October 28 agreement, including a United States demand that Soviet light bombers be removed from Cuba, and specifying the exact form and conditions of United States assurances not to invade Cuba.