It probably did vary based on the field. In linguistics, communication theory and anthropology, for example, there was little official communication, but some little did pass through. The Soviets often managed to smuggle in the most important works of Western scholars and unofficial translations circulated among secret scientific societies (e.g. the Tartu-Moscow School of semiotics). Since they had to stave off KGB and their informants, outside information was often distributed in 18th century salon gatherings (which were very popular and influential in Russia especially), e.g. a distinguished person invited friends and acquaintances to his or her home. The reverse is also true - Soviet manuscripts were often smuggled out to be translated and published in Western journals. More often than not, though, they were published in departments of slavistics, so that Soviet film studies, for example, didn't actually have much influence on Western film studies. It was also the case that the French were much more it tune with Soviet humanitarian fields, perhaps because they were more openly Marxist, so that the French were often mediators between America and Russia. For example, the concept of "intertextuality" was originally Mikhail Bakhtin's term but gained notoriety through Julia Kristeva. So, too, with structural anthropology, which is attributed to Claude Lévi-Strauss, but only came to be because of the influence of Roman Jakobson. There are countless such examples, but they are easier to trace on the Western side, because the Soviets didn't cite or reference their Western sources. Also, during the Khrushchev Thaw, some few Western academics did get to travel into Soviet countries, especially for conferences, but were kept on a tight watch and driven around by KGB officers.

Source: am Estonian, e.g. from an ex-Soviet satellite country.