Russia had the largest part of the Soviet Union. Through most of the final half of the 20th Century, the United States and the Soviet Union (known also as the USSR) were the principal actors in an epic battle, referred to as a Cold War, for global domination. Cold War was a state of extreme unfriendliness existing between countries, especially countries with opposing political systems, that expresses itself not through fighting but through political pressure and threats. The expression is usually used of the relationship between the US and the Soviet Union after the Second World War.
The factors that led the relationship of US and Russia evolve into a Cold War were:
Firstly, Politically and Ideological differences as the Soviet believe in Communism, with Central Economy style, US believe in Democracy, with Capitalism style which clearly challenges each other.
Secondly, Mutual distrust. While US was planning to drop the atomic bomb on Japan, the US told all the WW2 allies except USSR (Soviets) before the actual bombing even though USSR was part of the WW2 allies. This made Soviets suspicious of whether to trust US or not as its possible that US might attack them in similar way.
Thirdly, the foreign policy objectives of the USSR were similar to the Russian monarchy-such as an Eastern European buffer zone in order to prevent Wars from taking place and a warm-water port not located on the Pacific Rim. However, they stationed troops from Russia till the Eastern Germany, that was far from Russia and all of them were turned into a Communist Government and listened to Russia promptly without questioning because the elections held by Soviets were not free and fair. Hence, US thought that the Soviets were going to dominate the whole Europe or even the World.
This thought threatened US.
Both sides were armed with enough nuclear warheads to destroy each other as well as would affect the lives of innocent people. Both sides had the seeds of conflict inherent within their own political systems. The US and the Soviet simply watched each other’s move. It was a game of “Up the Ante” on each other.
Lastly, the US president, Truman , had a Domino theory that beliefs if a country falls into Communism, the neighboring countries would again, fall into communism and spread it to the whole world even without the “buffer zone”. This had resulted into US supporting South Vietnam (Republics,Democracy) and on the other hand,USSR and PRC (People’s Republic of China or the Mainland China- NOT Taiwan which is Republic of China, ROC) supports North Vietnam (Communist,Socialism) in Vietnam War that resulted loss in US and the South that led to a reunification in Vietnam because the US fear that the North might spread Communism into the Whole South-East Asia. Also, the Korean War had the similar result, except that because of lack of USSR support, it had led into a draw.