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The Cold war is the term for the buildup and tensions between the two global superpowers post WWII, the U.S and Russia. While no direct conflict took place between the two, a number of proxy wars were fought between the two. The perfect example is the Chinese Civil War. Neither side fought in it, but both the U.S and Russia supplied the opposing sides with weapons, food, etc...
The other side was the buildup of weapons between the two sides. Both trying to gain a significant military advantage of the other. Which was impossible because neither side even knew what the other side had, and were basing their massive military spending on paranoia about the other side.