The Union of Soviet Socialist Republics (U.S.S.R.), commonly known as the Soviet Union, was a communist state in Eastern Europe and Asia, consisting of 15 Soviet republics: Kyrgyzstan, Tajikistan, Armenia, Belarus, Ukraine, Russia, Estonia, Latvia, Lithuania, Azerbaijan, Kazakhstan, Uzbekistan, Turkmenistan, Georgia, and Moldova. The country fought on the side of the Allies in World War II. The Soviets also offered assistance to Mao Zedong's communist regime in China in the early 1950s, until a breakdown in relations led to a state of ideological tension between the superpowers. This tension may have increased greatly due to dispute over Mongolia, a Soviet puppet state which the Chinese claimed as theirs. In the Fallout universe, the USSR did not dissolve in 1991, and continued to exist well into the 21st century, due to the divergence. This also leaves many of the country's affairs between 1945 and the Resource Wars period a mystery.
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, some citizens were still wary of the Soviet Union.
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 cautious of one another, keeping guard for a possible attack.  It is also not known when China overtook the USSR as the main adversary of the United States. The rise of China could also have led to closer ties between the US and the USSR.
When R. Scott Campbell was asked why China was the U.S. enemy and not the Soviet Union, he answered that it was because he heard the Russian mob firing their guns in the street while he was telephoning a Muscovite. After that, he had a difficult time believing that the U.S.S.R. would be in a position to threaten the world any time soon.
In Fallout 4, The Switchboard's research terminal, under saved transcripts dated June, 19, 2067 the USSR is mentioned in a 'USSR China Attack' Scenario.
In Fallout 4, Codsworth will talk about the "Red Menace" in a certain conversation path, when asked what he is talking about he will mention "The Russians and Chinese", implying that American society was just as mistrusting of the Soviets as the Chinese, as both were Communist nations.
In Fallout 4, when inspecting a bottle of Vodka one can notice that it is imported from Russia.
↑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".
↑The nuclear Armageddon in the back-story was between the US and China. After shipping several people asked me why China and not the old standby, the Soviet Union. I made the choice when I remembered experiences with Oleg, a Moscow developer I worked with months before when I was assistant-producing a typing game. Once, in the middle of a phone conversation, I heard some muffled bangs, and the phone went quiet. When I asked him what the noise was, he replied, “Oh, it was just the Russian mob firing their guns in the street.” I thought he was joking – he wasn’t. After that, I had a really hard time believing that the once mighty USSR would be in a position to threaten the world any time soon. So I turned to the next major communist country that typifies “the East”: China. 
↑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".