The U.S and Soviet Union competed through proxy wars across the world. Rather then engage in direct combat, they used their vast armies to send to smaller nations. The doctrine of MAD (mutually assured destruction) meant that the two superpowers couldn’t engage directly, or it would be nuclear Armageddon. These wars include the Yom Kippur war, Angolan Civil war, etc. Sometimes, the two nations got involved directly, like in Vietnam or Afghanistan, however, this was rare.