Some unspecified past war is mentioned as a background event. It is not certain if it was "World War III". America and Soviet Union/Russia are mentioned as opposing sides.
Even 3 years before the war, a special forces team under Willis Corto were training for a cybernetic assault against Russian facilities.
According to Julius Deane (who spent wartime in Lisbon) the war lasted only 3 weeks. He says that Case is probably too young to remember the War so it must have occurred around 20 years before Neuromancer. However McCoy Pauley and Elroy stayed more than a month in a POW camp in Siberia.
Squids were used to find submarines, suss out enemy cyber systems. The Navy employed "war whales" in the naval warfare and in minesweeping, addicted to heroin in order to control them; Jones had squid sensors to sweep enemy mines in the Pacific.
The US military leaders hid in the bunkers in McLean. Sites of operations were Leningrad, Kiev, Siberia where the present technology of hacking was invented. The operation Screaming Fist against the Kirensk computer nexus. The war ended 9 days later.
It is possible that Automatic Jack participated in the War; he was in Kiev, hang-gliding under a Nightwing parafoil, with a 50kg radar jammed between his legs. Then a Russian accidentally burned his arm off with a laser, amputating him.
There was a great postwar "political football, Watergated all to hell and back", when it was revealed that American intelligence knew about the Russians's EMP defenses; American soldiers were sacrificed as "turkey shoot for Ivan" to test some new technology.
within 11 months after the end of the war the Pentagon and the CIA were partially dismantled, divided to warring factions. Congressional investigation focused on the Screaming Fist fiasco, and there were show trials in Washington and McLean. A Congressional aide found Colonel Corto in a hospital and made him testify; a Congressional cabal with certain vested interests in saving particular portions of the Pentagon infrastructure gave him a testimony in favor of 3 officers who withheld information.
The prototypes of the programs developed for Screaming Fist continued to be used by hackers to crack industrial banks. The Mole series was the first generation of real intrusion programs (icebreakers). Squids are used to break brain chips. Ratz wears a mechanical arm of military Russian technology, potentially recieved in a PoW camp
Many former special Forces became cops or corporate security.
The videogame Tank War Europa may be based on the War.
Considering that Gibson's works were written in the '80s and the opposing sides are US and Russia, it is possible that the war was envisioned as the culmination of the Cold War, projected into the future. It was impossible to predict that the USSR would dissolve in '91 and the Cold War would end.