The battle over the Nobel didn't end with Bunin and Gorky. Volkov describes four subsequent battles, the most famous perhaps that of Pasternak, who was awarded the Nobel prize for literature in 1958 but was forced by Krushchev to decline. Pasternak died two short years later, but left a rich legacy, which Alexandr Sholzhenitsyn took to heart.
Meanwhile, the Soviet Union got its first official winner in Michail Sholokhov, best known for Quiet Flows the Don. Sholokhov had been a favorite of Stalin but it wasn't until 1965 that he became a Nobel laureate. Volkov feels that this was more or less a concession to the Soviet Union, after the Soviet premier through over Pasternak, who probably would have never been recognized if it wasn't for all the drama that surrounded the smuggling of Doctor Zhivago out of the Soviet Union in 1957, a book Pasternak couldn't get by the censors. The Don Flows and Doctor Zhivago are generally recognized as the two best Russian novels of World War I, more or less in the tradition of War and Peace. Zhivago wasn't printed in the Soviet Union until Gorbacev's Perestroika. Quiet Flows the Don was made into a memorable film by Sergei Gerasimov in 1957, and remade by Sergei Bondarchuk in 2006 with an international cast.
The next big battle came in 1970 when the Nobel committee awarded the dissident writer Solzhenitsyn, who was surprisingly allowed to accept the award. He later stole a page from Pasternak and smuggled The Gulag Archipelago out of the Soviet Union, which was subsequently printed in France, England and the United States. Solzhenitsyn had spent time in the infamous Lubyanka Prison and imagined a series of books describing his experiences in a similar vein as Chekhov's Sakahlin Island, calling attention to the penal colonies spread around the Soviet Union. He smuggled much of the handwritten manuscript out of the country through the family of an Estonian lawyer, he had met while in prison. It created a huge furor and the Soviet Union planned to ship Solzhenitsyn off to the far reaches of Siberia but Western powers interceded and arranged for a transfer, which eventually led to the dissident writer being settled in Vermont with his family, who had fled the country years before. There is a relatively recent documentary on the story behind his most famous book, which you can watch at blinkx in its entirety.
By comparison, Josef Brodsky's Nobel prize in 1987 seemed anticlimactic, but he underwent quite a show trial in 1964, which led to his deportation in 1972, and settling in New York. Volkov met up with him in Manhattan and in time published their conversations between 1978-1992. There was a wonderful movie, A Room and a Half, made in 2010 on Brodsky.