There've been a few posts here already about Russian music, but I wanted to bring up something I was wondering about for a while (and learned a lot about from one of Dr. Denner's tangents): the underground Soviet rock scene.
Rock bands started appearing in Russia about as soon as Russians were able to listen to smuggled rock from the West and emulate it. By the mid-1960s, people across the USSR were listening to smuggled or pirated Beatles and Rolling Stones records and yearning to imitate the sound and spirit of the new genre; surprisingly, Beatlemania hit the Soviets about as hard, if not harder, than Westerners. Just about every Soviet rock group I looked up, no matter what it sounded like, considered the Beatles to be its primary influence.
The first underground genre to gain prominence in the 1960s was the so-called "авторская песня" (author's song): acoustic sets performed by lone singer-soungwriters, usually referred to as "bards." One of the most famous of these bards was Vladimir Vysotsky, who was basically a Russian Bob Dylan, singing pseudo-poetry that was sometimes down-to-earth, sometimes absurd and occasionally politically poignant.
From the late 60s and throughout the 70s, the underground Soviet rock scene really blossomed, with famous bands such as Машина времени (time machine) and Аквариум (Aquarium) performing and privately recording a great deal of music. Most of these bands were apparently quite Zepplin-esque, but a wide range of styles were experimented with, including psychodelic and prog rock.
When I refer to this scene as "underground," it carries a lot more meaning than it does in the US, since rock music was banned in the USSR during this entire period. The country only had one record label, Μелодия, and music that wasn't culturally or ideologically sound wasn't considered acceptable for Soviet audiences and thus went unrecorded by the official music industry. However, the scene survived through the efforts of the artists themselves; performances were often held in peoples' apartments and in warehouses and basements, and since every other Soviet citizen was trained as an engineer, many had the technical know-how to record their own bootleg records. For example, Аквариум recorded their albums on an underground, self-built recording studio, and some bands would bribe Μелодия staffers for the secret use of their equipment. Since material for making records was scare, the music was usually pressed onto old x-ray plates; today, records in Russia are sometimes still referred to as рентгениздаты (X-rays).
Russian rockers were finally able to reap the benefits of their talent in the Gorbachev era, when censorship was loosened and some bands were able to officially record and appear on television. Today, the most prominent of the underground rock groups are recognized as iconic figures of Russian music; they'll never forget the people who risked their careers and lives just to keep on rockin' in the not-so-free world.