The tension between the US and Soviet Union lead to increased nuclear buildup during the mid to late 20th century. Even though these two countries were the ones facing off, it had an enormous impact on the rest of the world.
For example, America's nuclear capabilities increased dramatically during the Vietnam War. Since the US was involved in helping to keep Southern Vietnam free from communist rule, the threat of nuclear warfare scared Vietnamese citizens.
Another example would be the alliances formed during this era. The US had several military allies thanks to the North Atlantic Treaty Organization. The Soviet Union had military alliances as well, thanks to the Warsaw Pact. These countries aligned with the US and Soviet Union could become possible nuclear targets for the rival country.
