How did the Korean War start?
The Korean War started with North Korea (Communist) invading South Korea (non-Communist) early in the Cold War. The aggression of North Korea caught the attention of the United Nations. This caused the U.S. to immediately assist South Korea with heavy military and the Soviet Union do the same with North Korea
The War
North Korea invaded South Korea because South Korea was non-Communist and Stalin promised assistance for an invasion. This made the UN assist South Korea from communism. The US sent a heavy military force to help them, but by the time this happened, North Korea had already taken Seoul, South Korea's capital. This was a dangerous situation for the U.N.
President Truman tried to use his atomic weoponry to U.S. advantage in North Korea, but he was never able to. It was not even clear that atomic bombing in a war against weak armies would produce major results in a war like this. If the Americans used the bomb and the Soviet forces kept on coming, it would show the bomb is ineffective and the enemy would not feel threatened.
For nearly two years there was talk of a cease-fire between North Korea and South Korea and their allies. An agreement was starting to settle faster due to Stalin's death. It all finally came to an end on July 27th, 1953. There were catastrophic damages because of the war. 4,000 tons of bombs were dropped by Strategic Air Command in just the first month of fighting. Although it was an end to a bloody war, it was only a preview of the Cold War.