During the late 1950s and throughout the 60s, the Soviet Union and the United States carried the Cold war into space. It was a battle for who was the best at new technology.
The Soviets were first to get a spacecraft launched Sputnik in 1957, and to get a man into space Yuri Gagarin, in 1961. But then the Americans were the first to get a man on the Moon, in 1969.