There are a number of events that occurred during the Cold War that could be seen as proxy wars. In this context, a proxy war is a war in which one or both of the superpowers uses other countries or groups as its proxies to fight in its stead. This was one way that world leaders tried to keep the Cold War from escalating into a true war. They used proxies so that they would not have to fight one another.
In the Cold War, the United States and the Soviet Union were competing with one another for world dominance. Even though they were in competition, they never actually fought one another directly. This was largely because they were afraid such a war could spiral out of control. They did, however, fight one another indirectly, through proxies. The first proxy war was a civil war in Greece between communists and noncommunists. From the Soviet Union’s point of view, the Korean War was a proxy war. The US did not have proxies that it could use in that war since South Korea was too weak, but the Soviet Union was able to use North Korea (and to some extent China) to fight the US for it. Both the Soviet Union and China used North Vietnam as a proxy to fight the US in the Vietnam War.
In the Bay of Pigs invasion in 1961, the US was trying to carry out a small proxy war. It wanted to get Cuban exiles to fight so that it would not have to invade Cuba itself. The US also used proxies against the Soviet Union in Afghanistan in the 1980s. When the Soviets invaded Afghanistan, the US funded and supplied fighters known as the Mujahedeen who were fighting against the Soviets. These are some of the best-known proxy wars that took place in the Cold War.