What did the Cold War actually look like in orbit? It ran on three tracks at once: operational systems for intelligence, communications, navigation, and early warning; symbolic milestones — satellite, cosmonaut, astronaut — for public consumption; and the underlying rocket and satellite technology that made both possible. The R-7 that launched Sputnik was, in fact, the same booster that would have carried a Soviet nuclear warhead to the United States.
The operational contest included the American Corona program (operational August 1960), the Soviet Zenit series, GPS and GLONASS, and the American DSP and Soviet Oko early-warning constellations. These systems provided the foundation of the strategic balance that made arms control possible.
The symbolic contest had two phases. The Soviet Union dominated from 1957 to 1965, with firsts in satellite, animal, human, woman, and spacewalk. The United States dominated from 1965 to 1972, with the Apollo lunar landings. The most visible symbolic contest of the entire Cold War, the race to land a man on the Moon, was won by the United States with the Apollo 11 landing on 20 July 1969.
The symbolic and operational were tightly connected. The R-7 that launched Sputnik was the same rocket that would have carried a Soviet nuclear warhead to the United States. The Saturn V that launched Apollo 11 was the same family of rockets that would have carried U.S. nuclear weapons in a war. The public framing of the race as a contest of “firsts” obscured the operational reality. The Cold War in space has been succeeded by a different competition, with new participants (ESA, China, India, and the commercial sector), but the technological and operational foundations were laid in the 1950s and 1960s.
For the rest of the military space article and the space race overview.