Led by former Czech President Vaclav Havel, the Velvet Underground was an anti-Communist political party and a semi-annoying rock band that was well known for hanging out with Andy Warhol's friends while Andy himself was off "having an organza."
The band began to take issue with Havel's frequent inability to perform his band-fronting duties due to his nasty habit of getting stuck in jail for years at a time for "dissident" activities. So they decided that when Havel was "otherwise indisposed," they would let a crazy bisexual Jew, Lou Reed, front their revolutionary movement/art noise performance group. But this was not as successful for their movement, as they mostly cranked out demonic hits such as "Heroin", "Rock and Roll", and "Sweet Jane". Under Reed's leadership, the Underground created the phrase "Sex, Drugs, and Rock and Roll" and took this as the movement's motto. However, since this was most of what they did, they didn't do much of anything.
When Havel was finally released from jail for the last time in the 80's, the Velvet Underground got together for a reunion tour. They decided to return to their revolutionary, anti-Communist roots and started agitating for reform in Czechoslovakian political conditions. By the end of the decade, Havel was able to lead the Underground to the top of the charts and a "Velvet Revolution" was fully underway. Soon, the Communists would leave Czechoslovakia altogether, and the newly democratic state of Czechoslovakia would elect Havel its first president.
Later, when the band split up, Lou Reed became Prime Minister of Slovakia, while Havel remained President of the Czech Republic. Havel clearly got the better deal country-wise. Reed got Laurie Anderson, and Havel ended up with some Czech actress. You can decide who got the better deal there.