Korean War
The Korean War was a war during the Cold War. The US backed South Korean and the USSR backed North Korea. The north was communist and the south nationalist. They fought each other in second-hand combat. The country was split at the 38th parallel. Both sides pushed each way, but ended in the exact same spot as the start.
The US felt that the war was a success. It showed their win of containment over the USSR and their spread of communism. It was a victory for the US even though they lost so many men in the war. Marshall wanted to bomb China, since they came into the conflict, but Eisenhower fired him for spreading falsified rumors to the press.
The USSR did get to have another communist country, but not as much as they wanted. Overall a loss to them. The North was communist, but the south remained in a loose capitalist state.
This war was a big step in the Cold War. It was a time in which the UN was used, but its majority was the US, and it was a big turning point in which the Soviets were finally stopped with containment by the US.