Eliminating smallpox was probably the greatest global health victory of the last century, if not ever. It was made possible by remarkable cooperation between the United States and the Soviet Union of a sort which was rare in the Cold War. And it also, bizarrely enough, owed a lot to the Vietnam War.
The smallpox drive was carried out under the auspices of the World Health Organization, which was largely funded by the United States. The Soviets had refused to participate in the organization after 1948, claiming that it served a western agenda and didn't devote enough resources to the Communist countries. A similar boycott of the United Nations Security Council prevented them from using their veto to keep the western intervention in the Korean War from happening under a UN mandate, but it took until 1958 for the Russians to decide there might be benefits for them in dipping their toe back into the WHO. And it turned out there were benefits for the rest of humankind, too.
At the time, the United States was invested in a costly and largely ineffective campaign against malaria under the rubric of the WHO. The Soviets, who happened to have most of the world's smallpox vaccine manufacturing capability, pointed out that the efforts of the global health body might be better directed towards smallpox: it was theoretically possible to vaccinate everyone in affected areas and wipe the disease out, whereas mosquitoes could continue to carry malaria indefinitely. The American anti-malaria campaign was actually based on the idea of wiping out mosquitoes, and the Soviet proposal seemed workable by comparison.
However, it took a while for the Americans to come around to the idea. The late 1950s and the early 1960s were a fraught time in the Cold War, a madness that culminated with the Cuban Missile Crisis. The U.S. didn't want to be upstaged by the Soviets, or admit its malaria campaign was misguided - so it told the Soviets that if they were really so serious about global health, they ought to get behind the malaria campaign rather than making silly suggestions.
This stance remained the official line for some years. But three factors gradually intervened. First, the deficiencies of the malaria campaign became obvious. Secondly, tensions between the two superpowers eased. Lastly, the United States realized that the Vietnam War was given it a major public relations headache, and decided to do something about it.
One way to understand the Cold War is as a battle between the Americans and the Soviets for the allegiance of the global south. Both wanted to export their model of civilization, and to demonstrate to countries across Asia, Africa and Latin America that their way of life was best. Part of this was showing off their goodwill and their technical abilities. When the U.S. was faced with a probable Communist takeover of all of Vietnam, it responded with brutal firepower, and it worried that this might damage its image across the rest of the world.
Lyndon Johnson, the American president who decided to escalate the war in Vietnam in a major fashion in 1965, was a liberal who constantly wrestled with his conscience over the war. He liked to see the war as one engagement in the battle to provide a non-Communist route to prosperity and development for Asia and Africa, and he was keen to open other fronts in the war as well. So another decision his administration took in 1965 was to throw the weight of the United States firmly behind a campaign to eradicate smallpox.
Not only did this mean acquiescing in the Soviet call to make smallpox eradication the key thrust of the global health agenda, it also meant cooperation with the Soviets - they had the main sources of vaccine. Of the two billion doses eventually administered, the Soviets manufactured 1.7 billion. The U.S. provided most of the funding. By 1975, smallpox was eradicated.
The campaign against smallpox was not only an amazing example of mankind's ability to overcome an age-old challenge, but also set a precedent for the depoliticization of global public health. The UN has many critics, but the creation of a neutral, non-political space in the form of the WHO allowed politics to be put to one side and a great good done for humankind. Its scale was also telling, and an echo of it can be seen in the millions of people vaccinated against polio annually in India. And it showed what can be accomplished when the leading powers of the world work together, not against one another.
My main source for this write-up is Erez Manela, "A Pox on Your Narrative: Writing Disease Control into Cold War History," Diplomatic History 34:2 (April 2010), 299-323. For understanding related issues in the history of the Cold War as a whole, see Odd Arne Westad, The Global Cold War: Third World Interventions and the Making of Our Times.