At the end of World War 2, The Soviet Union took control of Eastern Germany and was a huge influence to other countries in Eastern Asia. They helped to start the spread of Communism.
Once Communism had become widespread over Eastern Europe, the US joined in to help stop it from spreading farther than it already had.
This sparked what was called the Cold War. The Cold War is considered a war but the US and the Soviet Union never fought directly with each other.
Other wars happened during the Cold War that both sides were involved in. They are the Korean War and the Vietnam War. The US supported the South Koreans in the Korean War and the South Vietnamese in the Vietnam War.
During the Korean War, the Soviets supported the North Koreans and supported the North Vietnamese in the Vietnam War. Both countries sent troops to help support the war effort for each side.