The Cold War
"After the end of World War II, the world was split into two -- East and West. This marked the beginning of the era called the Cold War"
- – Metal Gear Solid 3: Snake Eater
The European theater of World War II ended with a race by the western allies (mostly the United States) and the Soviet Union to reach central Germany and take over. A result of this was that while the Soviets took the capital and most Germany captures to the east, the west actually held the western half of Germany. During this the United States developed nuclear weapons. While too late to drop on Germany (as originally planned) they wound up using two of them to destroy the Japanese cities of Hiroshima and Nagasaki. Thanks to Franklin D. Roosevelt's utter shit anti-espionage standards, the Soviet Union learned of these before his own vice president did (Remember changed vice presidents because he knew he would die any day and his last one was an open Soviet stooge. Despite what they told you in school, FDR was a really shitty president.). Using their spies they promptly stole how to make these weapons themselves.
This wouldn't be much of an issue, as the Soviet Union was an unstable entity trusted by no one (their refusal to honor Russian debts and contracts meant nobody would trade with them) on the brink of financial ruin... was until FDR formally recognized and financially supported the Soviet Union in an attempt to throw as many bodies at Germany as possible while simultaneously propping up Chinese communists who used US assets to murder their rivals and take over the country to throw as many bodies at Japan as possible. Now the communists had a massive military, modern technology (including nukes), control of a massive chunk of the world. You expected thrice re-electing a guy that legitimately thought burning food would end famine to end in anything less of a global cluster fuck?
To counter this massive, nuclear armed force the nation of the North Atlantic signed a Treaty to create the Organization known as NATO in 1949. This military alliance held that any attack against one of them would be an attack against all of them and lead to STANdardization AGreements to ensure compatibility standards all members would meet. These included various steps to ensure compatibility of items like ammo and gas mask filters, but also communications and general conduct like how prisoners are treated. In practice this was mostly a threat of "you attack us, the US nukes you". Due to the whole North Atlantic thing Australia, New Zealand and Japan weren't included, though they followed many of the STANAGs and were on the list of places the US would respond with nukes if attacked.
The two sides realized that any attack would result in Mutually Assured Destruction (MAD) and avoided doing that directly. Instead conflict was conducted through spies and proxy conflicts where, using their newfound power, the communists would prop up other communist revolts across the globe. In response the United States would prop up their opposition, regardless of how blatantly evil they were. At least twice this went as far as outright military action by both sides during the Korean War and Vietnam War. In response to these proxy wars and people simply leaving their shithole by the millions, the Soviets built a large wall across their western border known as the Berlin Wall. They also had a falling out with the Chinese, which split the two.
Eventually this era ended from the Soviet Union imploding than anything else. In the late 1980s a series of revolutions in Soviet states would lead to East Germany giving up, opening the border and reunifying with West Germany within a year. This caused further turmoil in Russia by a failed coup that lead to the end of the Communist Party and fall of the Soviet Union. To generations that expected some world sundering conflict, this was underwhelming for most westerners. Those on the east of the wall are often a bit annoyed that decades of communism has left their economies severely stunted compared to the west (to this day, decades latter, eastern Germany is still far behind the west economically), and within Russia proper there is nostalgia for the Soviet Union (communism itself less so)
The appeal of the Cold War
The appeal of the Cold War in fiction comes mostly from the spy game. Since the end of the Cold War, the role of espionage has greatly fallen. If you want to do a work of fiction about spies and don't have a specific setting, it will generally involve the Cold War or at least former Cold War spies.
More generally there's a bit of nostalgia for the west having a clear enemy to stand against and one that, if you weren't a spy, you'd generally see coming. The CIA director after the end of the Cold War told Congress "We have slain a large dragon. But we live now in a jungle filled with a bewildering variety of poisonous snakes. And in many ways, the dragon was easier to keep track of." Now the main enemy is one half of politians and most entrainment production try to prevent being demonized (regardless of what it does) or being fought seriously. This enemy can kill thousands of civilians in a night and, not being a state, you can't send an army after them in response.
There's also appeal in the general military conflict of the era, but this mostly appeal of the Vietnam War as a setting and appeal of "what if all those cool toys NATO and the Soviet made actually saw use?".
Cold War inspired Games, Factions and Settings
- Anything set in the modern world that was made before 1991.
Cold War Gone Hot
- Team Yankee