The Union of Soviet Socialist Republics (U.S.S.R.), commonly known as the Soviet Union, was a pre-War communist state in Eastern Europe and Asia, consisting of 15 Soviet republics. In the Fallout universe, the USSR did not dissolve in 1991, and continued to exist well into the 21st century.
The Soviet Union had a consular service and a foreign service, and had strong consular relations with the United States. There was a Soviet consulate in Los Angeles (the one Natalia's grandfather worked at), suggesting that Soviet-American relations were good enough in 2077 that American and Soviet citizens were able to visit each other's countries. However, in propaganda, the Soviet Union was still being portrayed as a 'communist enemy'.
During the Resource Wars, the Soviet Union was in no direct conflict with the United States. It is unknown what role they played in the Great War, although both sides were still wary of one another, keeping guard for a possible attack. 
↑In the Helios One terminal entry "Can I Tell Him?" urging complete secrecy, A hypothetical situation is presented that results in the USSR acquiring national secrets, with "Ivan Bullykov will get more than lunch money out of your kids. He'll have national secrets! And while they're parading him through Red Square as a national hero, your children will be working in forced labor camps, right next to you and your beautiful young wife".
↑In line with Marxism, communism has never been implemented because for communism to exist the state must be dissolved and be proceeded by a worldwide socialist phase, the U.S.S.R. was in fact a state socialist system, a so called "dictatorship of proletariat".