The Red Army was the name of the army of the Union of Soviet Socialist Republics. It was the name used mainly before and during World War II. After the war it was renamed as the Soviet Army, although many people still continued to call it the Red Army. Even nowadays some people still nickname the modern Russian Army as the Red Army.
Some later Communist organizations such as the Red Army Faction used the name, and anti-communists sometimes used the name for any left-wing group which they said was trying to promote communism and was paid for by the USSR.