Asociopolitical, military, and economic conflict between the western world and its eastern communist regimes from the end of wwii through 1991.

You are referring to the Cold War (1946-1991), which was primarily a political confrontation between two sides, the Eastern Bloc (the Soviet Union and its allies, which were communists) and the Western Bloc (the United States and its allies, which were capitalists). Each bloc aimed to achieve political, economic and military supremacy worldwide. Since there was no major or large-scale fighting, the conflict has been designated as cold.

This long (and indirect) conflict ended with the dissolution of the former Soviet Union (USSR) and the elimination of communist regimes in Eastern Europe and in other parts of the world. Furthermore, the United States came to be the world's main political and economic power.