Abstract: Recently sum-frequency has become a very powerful experimental technique in studying structures and dynamic of molecules on surface or molecules between surfaces. In this talk after brief discussion of the derivation of SFG, various possible types of vibrational and electronic SFGs will be discussed including the derivations of their quantum mechanical expressions based on the Born-Oppenheimer adiabatic approximations. In both electronic and vibrational SFGs, they can be classified into resonance-off resonance, off resonance-resonance and resonance-resonance SFGs (that is, double resonance). This will be followed by the discussion of their applications.