  We review recent progress in the study of non-rational (boundary) conformal
field theories and their applications to describe exact holographic backgrounds
in superstring theory. We focus mainly on the example of the supersymmetric
coset SL(2,R)/U(1), corresponding to the two-dimensional black hole, and its
dual N=2 Liouville. In particular we discuss the modular properties of their
characters, their partition function as well as the exact boundary states for
their various D-branes. Then these results are used to construct the
corresponding quantities in the CFT of the NS5-brane background, with
applications to Little String Theories.
