Reposting an answer which was deleted for a lack of a source: Duran Duran was explicitly banned in 1984. Yet there were fans around according to my parents. My parents is not a proper source, so that so take it for what you will. What follows is a source for the ban - the prikaz which explicitly mentions Duran Duran along with many other bands as music banned from Soviet Discotheques for «propagating bourgeois ideology».

Hа основании приказа N 361 от 25.07.84 «Об упорядочении деятельности ВИА и повышении идейно-художественного уровня их репертуара в свете требований Июньского /1983 г./ Пленума ЦК КПСС», в целях усиления борьбы с влияниями буржуазной идеологии, повышения идейно-художественного уровня самодеятельных ВИА, рок-групп, качества работы этих коллективов рекомендуем запретить проигрывание и демонстрацию в г. Москве грампластинок, компакт-кассет, видеороликов, книг, плакатов и другой продукции, отражающей деятельность следующих групп:

1. Hемецко-польская агрессия

2. Hемецко-американская дружба

3. Рейнгольд

4. Центральный комитет

5. Отсутствие цвета

6. КГБ

7. Кремль и хороший народ

8. 1948 год

9. Злата Прага

10. Белый Кремль

11. Черные русские

12. Россия

13. Кожаные комиссары

14. Петроградское ревю

15. Блю Ойстер Калт

16. Рамонес

17. Диагноз-403

18. Вероника Фишер

19. Хольгер Биче

20. Фигура

21. Кисс

22. Эрик Ланг

23. Пропаганда

24. Ди пресс

25. Скиф

26. Hина Хаген

27. Б-52

28. Стикет

29. Мэднесс

30. Секс пистолз

31. К л э ш

32. Стренглерз

33. Крокус

34. Айрон Мэйден

35. Джудас Прист

36. АС/ДС

37. Спаркс

38. ЮФО

39. Блэк Сабат

40. Элис Купер

41. Ху

42. Скорпионз

43. Чингиз Хан

44. Пинк Флойд /1983 /

45. Токин'Хедз

46. Церрон (т.е.«Черроне»)

47. Ла Бьонда

48. Джуниор Энглин

49. Кеннет Хит

50. Ван Халлен

51. Язу

52. 10 СС

53. Блонди и Дебора Хари

54. Хулио Иглесиас

55. Патти Смит

56. Элвис Костелло

57. Майкл Джексон

58. Дюран-Дюран

59. Род Стюарт

60. Ганимед

61. Хот «АС»

62. Милк энд Хани

63. Черри Лейк

64. Крафтверк

65. Hазарет

66. Дэнсинг Мод

67. Вилладж Пипл

68. Студжис

69. Бойз

70. Санта Эсмеральда

71. Мьюзик Мэшин

72. Оридженела

73. Пэссинжерз

Hopefully you won't mind if I provide a perspective not from the Soviet Union, but from socialist Czechoslovakia.

There seems be a misconception amongst younger people or those unfamiliar with that part of the world at the time that the eastern bloc was literally behind an impenetrable iron curtain and no semblance of 'Western' culture penetrated it. Nothing could be farther from the truth, albeit accessing it could prove difficult. The popular notion of a black market and friends lending and copying variously obtained records is of course correct, as that was one way of getting foreign music. Not because of official bans – although like many aspects of life under communist rule its sale was regulated – but rather due to convenience, as these records were in short supply.

So yes, being lucky or having a friend behind the counter did help, but you could simply walk into a store and buy a Bob Dylan vinyl, a Simon & Garfunkel tape, or, if your taste is especially refined, Barbra Streisand's debut album. Many foreign records were licensed and sold by Czechoslovak state companies, Supraphon and Opus. The former remains an active music publisher to this day. Apart from individual albums, compilations were also fairly popular, both as collections of songs of a particular genre, or 'mixtapes' by a single artist.

I am not aware of what the official selection process was, or what role, if any, political influence or censorship played in it. If I had to speculate, then going by the rather decent variety of released records I would suspect it was rather mild, perhaps only actively avoiding the harder parts of rock'n'roll, which is where the unofficial channels would come into play.

But you can judge for yourself – if you open this document (in Czech) and scroll down a few pages, you can see a list of foreign albums released by Supraphon and Opus in socialist Czechoslovakia. Note that it is not comprehensive by any means, for example it does not mention Joshua Tree by U2 or Bruce Springsteen's Born in the USA, but it should give you an idea as to the extent of 'Western' music that was officially available. Jimi Hendrix, Elvis Presley, David Bowie, Pink Floyd... all there. And yes, even Duran Duran.

You may want to ask this in /r/Russia too

Question, and hopefully it's not too late, but what music were the soviets producing at the time? I know most if not all western music was banned but what was the legal alternative? Did the soviets have their own "pop" music scene and what was it like?