At the end of World War II, Korea was divided at the 38th parallel. America and the Soviet Union stepped in to help out.
UN troops still pressured Koreans in to North Korea by force. Chinese felt threatened. Began to fight back. The Chinese outnumbered the UN troops and was able to push them out of north Korea.
McAuther resulted in calling a nuclear attack on China which was quickly shot down by Truman who thought that McAuthers plan was reckless where he says "We're trying to prevent a war not start one". McAuther was later fired.
Domino theory was an idea proposed by President Eisenhower that stated if one country would fall to communist ways, than other countries would follow.
Vietnamization is a plan by Nixion which allowed troops to slowly withdraw from the war. To pursue this plan a bombing campaign against North Korea was put into place.