Story is Short -
Russia plants Nuclear Warhead in Cuba which is 90 miles from US. What should US do? If it goes for an attack, a nuclear warfare could start. If it does not, it would be a big political defeat for Kennedy.
Somehow the crisis resolves, as we can see. But it came to be known only in 2002 after the secret military information was declassified that it was not Kennedy (US) or Khruchshev (Russia) who saved the world. It was an unknown submarine officer.
09/1962 - 27/10/1962 - 28/10/1962 - 23/04/1963
During Cold War (matches with the dates of Sino-India conflict)
US Prez - John. F. Kennedy
Russian Secretary - Nikita Khrushchev (This is a guy's name!)
Movie and Book: Thirteen Days
What Happened - In short
1. US is likely to invade Cuba
2. Russia plants nuclear warheads in Cuba and then lies to US that the equipments at Cuba are defensive and not offensive
3. US is all furious. In its first meeting decides that cuban invasion is the only option, but Kennedy is skeptical and says that this would clear the way for Russians to Attack Berlin, and pose Americans as 'Trigger Happy Cowboys'
4. McNamara (US def. Secy) says that putting 40 extra warheads does not change the military balance at all. However, it was observed by Kennedy and other that it changes the apparent political balance which would then threaten the real political balance (US - Russia)
5. The earlier imposed blockade of naval vehicles to Cuba (pt. 3) was converted to quarantine which is known in international terms as WAR
6. It was suggested that US removes the missiles it has in Russian neighborhood - Turkey. Though this was genuine, it was known as a trial balloon for a long time
7. US moves to DEFCON 2 for the only known time in history
8. Friedel Castro on the other hand was all set for a full blown nuclear war against US at the first sign of US invasion
9. Turkey meanwhile continuously stated that they were unhappy with this 'missile withdrawal thing'
10. Meanwhile Khrushchev made it clear that the US missiles in Turkey was THE thing. Russia will vacate Cuba and US should vacate Turkey. On the previous day Khrushchev had offered that Russia would withdraw from CUBA if US agrees to never attack Cuba again.
11. On 27/10 a US U2 plane was shot down while surveilling over Cuba. US had decided that in such case it would go for all out war, but they thought it might have been a mistake and decided against it. Russia after a short while confirmed that it was a mistake and ordered no more shooting down of U2s
12. EXCOMM pursuaded Kennedy to make the first offer to Russia - that of never attacking Cuba again. After much deliberation Russia accepted it and the crisis ended
13. Cuba was unhappy of the whole development as the entire conversation was b/w US and Russia and their opinion was not taken. This lead to sour Russia-Cuba Relationship in years to follow
14. The entire crisis was viewed as a political defeat of Khrushchev. However, it was because the US commitment of removing missiles from Turkey was kept Secret.
15. It was learned by the world in 2002, that it was on 26/10/1962 that the USS Beale had tracked and dropped signalling depth charges on the B-39, a Soviet Foxtrot-class submarine which was armed with a nuclear torpedo. Running out of air, the Soviet submarine was surrounded by American warships and desperately needed to surface. An argument broke out among three officers on the B-39, including submarine captain Valentin Savitsky, political officer Ivan Semonovich Maslennikov, and chief of staff of the submarine flotilla, Commander Vasiliy Arkhipov. An exhausted Savitsky became furious and ordered that the nuclear torpedo on board be made combat ready. Accounts differ about whether Commander Arkhipov convinced Savitsky not to make the attack, or whether Savitsky himself finally concluded that the only reasonable choice left open to him was to come to the surface. One of those
ACTUALLY SAVED THE WORLD!
p.s. incidentally, these dates collide with the India - China war of 1962. More details on the war to be found in my Laddakh post here