In this paper,we survey interesting results on CM values of special functions that come from reg-ularized theta liftings.We focus on modular functions which are Borcherds liftings and higher green functions which are regularized theta liftings.We also describe the basic ideas behind these beautiful formulas.They are the generalization of the well-known Gross-Zagier formula on singular moduli and their algebraicity conjecture on the CM value of higher Green functions.We skip the generalization of their most famous Gross-Zagier formula in this survey although the generalization also fits the idea of this paper.The method described in this paper is different from Gross and Zagier's original idea.
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