The Cuban Missile Crisis was a unique event in world history. It gains this status by being the climax of the period in human history when the threat of the complete annihilation of humanity was an everyday reality. The intrinstic importance and profundity of this event seems belied by descriptions of the banal bureaucratic and tactical happenings which constituted it. This is until you realize that its profundity lies entirely in the fact such processes could, if they'd gone wrong, have obliterated mankind.
It all began in May 1962, when Nikita Khrushchev took the decision to send medium-range ballistic missiles (MRBMs) to Cuba. It's not possible to entirely know his objectives, but we make pretty accurate guesses. The missiles actually made very little difference to the balance of power in strategic terms, i.e. the ability of the USSR to deliver nuclear damage to the USA. The USSR still couldn't carry out a debilitating first strike, and its strike capacity wasn't massively increased by the move. Rather, it was more a political affirmation of Soviet power, an attempt by the Soviets to demonstrate they were on equal global political parity with the USA. If America could station missiles in Turkey, so the Soviet logic went, then the USSR had a right to station missiles in Cuba. This option was even more attractive because it would help Cuba defend itself.
The Castro regime held a special place in the heart of many Bolsheviks. It was the only country on the planet to have gone Communist and enter the Soviet bloc without the imposition of the Red Army. It was also the only Communist nation in the Western Hemisphere. Only 90 miles from the coast of Florida, the Cuban regime was a sure signal to the Soviets that nowhere in the world was safe for capitalism any longer. They were especially keen that the flower of the revolution in Cuba not be squashed by the Americans, who had attempted to overthrow the Castro regime at the Bay of Pigs.
The Soviet military build-up in Cuba was not limited to strategic weapons. Also involved were 50,000 Soviet troops, Il-28 nuclear bombers, nuclear submarines and 100 tactical nuclear weapons (used on the battlefield). Clearly this couldn't proceed unnoticed, and even before the 15 October discovery of the MRBM launch sites the US knew something was afoot. However, sadly a partisan issue was made out of it. Republicans in Congress angrily denounced Kennedy's acquiesence in the Soviet military build-up, and JFK continued to deny the magnitude of the deployment. Indeed, its full scale would not be known until the opening of Soviet archives in the 1980s. This is lucky, because had the scale been known then the crisis would undoubtedly have been more serious - the withdrawal of the tactical nukes, for example, would be almost impossible to verify. Mistrust might have stymied an agreement.
The Soviet infiltration operation had been carried out with honed skill, as befitted a military that had now spent over fifteen years creeping where it was not wanted. However, it was nigh on impossible to hide the missile bases from U-2 RECON planes. Combining pictures taken with base construction manuals leaked by Colonel Oleg Penkovsky, America's premier Cold War spy, a positive identification could be made of the MRBM sites only hours after the photographs were taken. They also allowed the Americans to see that the bases were not yet operational, giving crucial time to act. This was the first miracle of the crisis, meaning that rather than leaping straight to offensive action the administration sat down and considered its options.
The strategy eventually decided upon was a blockade of Cuba, to which the Soviets responded with nothing more than a political offensive by denouncing it in their propaganda. As the blockade had the approval of the Organization of American States, Soviet denunciation proved ineffective. This blockade went into effect on 22 October, and many Soviet ships immediately turned back or changed course. The Russians were not keen on the thought of the Americans capturing a ship with their latest military equipment onboard, and nor were they willing to escalate the incident by commencing military action - especially when the MRBM bases were not operational.
The reality was that Soviet leader Khrushchev was in a bit of a bind. He had taken this risk partly to appease those in his inner circle who believed he was too soft on the West. This meant if he was going to back down he'd need an excuse, or he risked being overthrown by hard-liners. Some members of the Soviet Presidium (analagous to a Western Cabinet) had fallen for their propaganda in believing the USA was planning a decisive and cataclysmic confrontation with the Communist world - and they wished to steal a march by striking first. Khrushchev, by a process largely closed to us, managed to overrule those who were willing to risk local or general war over Cuba.
He was helped by faulty intelligence he received suggesting the US was planning to invade Cuba on the night of 26 October. This threw the reality of the situation into sharp focus for the Soviet side, as an invasion of Cuba was bound to result in general war. At this point he ordered a stand down and started pushing hard for a diplomtaic solution. It seems that the local commander who ordered the shooting down of the U-2 RECON on 27 October had sour grapes, but luckily this didn't lead to any further escalation.
Khrushchev's demands were telling - first, a pledge by the United States not to invade Cuba and secondly, the withdrawal of nuclear missiles from Turkey. This second demand was kept secret from the world, so it appeared to most that the Soviet leader had merely backed down (the non-invasion pledge wasn't considered a significant gain, because most of the world realized the USA wasn't going to invade Cuba anyway). In fact, the Soviets had gained a small quid pro quo, but that this outcome was seen as unfavourable was shown by Khrushchev's overthrow shortly afterward.
To conclude, all diplomatic histories of the Cuban Missile Crisis make it sound like the outcome was always safe. It's often stated that Kennedy and Khrushchev held the fate of the world in their hands, but anyone who has seen Dr. Strangelove might pause to think otherwise. The crisis put power in the hands of multiple men, and fate herself, to bring about nuclear war. One example is illustrative. Before the crisis, the CIA was running a program called Operation Mongoose designed to destabilize the Cuban regime by aiding exiles with an axe to grind. On 7 October one such group of exiles decided, entirely on its own authority, to blow up a factory. What if they had attacked a missile site?
Luck played a decisive role in this encounter, which made the introduction of those red telephones afterward even more comforting. Both powers had come so close to the nightmare of nuclear holocaust that they blinked, woke up as if from sleepwalking, and pondered how they'd got in such a state. We wouldn't be here today if this defining moment in the history of the world had gone even slightly wrong.
The story of the crisis is told well in James A. Nathan, Anatomy of the Cuban Missile Crisis (Westport CT, 2001) and more briefly in Norman H. Finkelstein, Thirteen Days/Nineteen Miles: The Cuban Missile Crisis (New York, 1994).