\indent it is widely known the classical poisson-boltzmann theory fails to describe electrostatic interactions in the cases of multivalent counterions, highly charged surfaces, and low temperatures, as the theory ignores many-body ion-ion correlations. surprising phenomena due to correlation effects include the charge inversion and the attraction between two likely charged colloids, both of which are recent focuses of theoretical and experimental study. in this talk, we will present some theoretical and simulation results on these problems by studying the role of image charges on spherical colloids, and discuss the method to include the correlation effects in the mean-field pb theory.