1) Western Marxism: the obscure German or Italian intellectuals who had been defeated by official communism, but continued to proclaim themselves spokesmen for a certain kind of intellectually consistent radical Marxism. The rediscovery of these dissenters allowed academics and intellectuals to place themselves in a line of dissent from a respectable form of Marxism separate from the Soviet Union.
2) Young Marx:
This means sharing the renewed appreciation for Marx the philosopher; Marx the theorist of alienation. The advantage of discovering young Marx was that he furnished you with a whole new vocabulary. Marxism becomes a more diffuse language accessible to students and serviceable for substitute revolutionary categories - women, gays, students and so on. Such persons could now be readily inserted into the narration despite having no organic link to the blue collar proletariat.*
3) Claim historical processes have moved away from Europe and the Soviet Union itself and focus instead on the Chinese revolution and the rural revolutions then under way in Central America, East and West Africa and South East Asia.
The second of these three positions, the vocabulary of the young Marx, is the more significant of the three because much of the content of modern day sociology is drawn from this intellectual seed motivated by the forced retreat from the soviet project.
*Tony Judt, Postwar.