  We review and extend recent attempts to find a precise relation between
extremal black hole entropy and degeneracy of microstates using AdS_2/CFT_1
correspondence. Our analysis leads to a specific relation between degeneracy of
black hole microstates and an appropriately defined partition function of
string theory on the near horizon geometry, -- named the quantum entropy
function. In the classical limit this reduces to the usual relation between
statistical entropy and Wald entropy.
