Electrons in clusters of galaxies interact the passing photons of the cosmic microwave background radiation field through the inverse Compton scattering, which is called the Sunyaev-Zel'dovich (SZ) Effect. As it is redshift-independent and insensitive to detailed structure, it provides a powerful probe for studies of distant clusters of galaxies and their evolution. The under-constructed no-target SZ effect  cluster surveys will best constrain cosmological primary parameters. Summarizing the SZ effect and quantitatively analyzing all kinds of uncertainties in the theoretical prediction of the SZ cluster counts are very important for precisely determination of cosmological parameters. It is crucial to evaluate the uncertainties in current theoretical prediction before applying it into future SZ surveys.