Unlike the two world wars, there were no physical battles between the major adversaries. It was, instead, an extended competition between the United States and the Soviet Union, along with their respective allies. In 1991, the Soviet Union split up into 15 countries, the largest of which is Russia.
Indeed, as LaFeber notes, the era of the Cold War was far from a peaceful time when seen in a broad perspective; it witnessed over 40 million human casualties across territories. The experience of bipolar politics certainly varied in intensity and in temporality across regions.