Interesting nonperturbative CFT dualities like the FZZ duality between the 2d black hole and Sine-Liouville can be understood as a combination of two remarkable phenomena: The first is the modular (self-)duality of Liouville or conformal Toda theory, the second is the relation between Liouville theory and the sl_2-WZNW model. The latter can be seen as a natural "quantum" analog of the geometric Langlands duality. It may be reformulated as a correspondence between quantum Teichmüller theory and the sl_2-WZNW model.