The Cuban Missile crisis was when the USSR placed missiles in Cuba. The United States was not happy with having nuclear bombs so close to its territory, so they blockaded Cuba. The United States and Soviet Union eventually came up with an agreement that all USSR missiles would be removed and then America would not invade Cuba while Fidel Castro was president.
The Korean war started when North and South Korea physically split. It was supposed by the United Nations, China, and the Soviet Union.the United States tried to convince the UN to end the war because it had most of the world in fear of what would happen, especially considering North Kore's power. Both America and the USSR also wanted to take over the Korea's.