Final answer:
The competition between the United States and the Soviet Union after World War II was called the Cold War, a period of political, military, and ideological rivalry that did not result in direct military conflict but saw many proxy wars.
Step-by-step explanation:
The competition between the United States and the Soviet Union after World War Two was called the Cold War. This period of tense geopolitical rivalry began at the end of World War II in 1945 and lasted until the collapse of the USSR in 1991. The Cold War was characterized by the struggle for global influence and power, seeing the world divided into two major spheres of influence.
Despite the immense military buildups and the ideological contest, this era did not result in direct military conflict between the superpowers, largely due to the deterrent effect of Mutually Assured Destruction (M.A.D.) from their nuclear arsenals. Throughout the Cold War, there were many indirect conflicts, often referred to as proxy wars, where the United States and the Soviet Union supported opposing sides.