in this talk i will give an overview of the recent development of boundary integral methods for solving poisson-boltzmann equations (pbe) for the electrostatic potential in a solvation system of biomolecules. electrostatic forces are crucial in determining the structure and dynamics of biomolecules and their interactions with solvents. as a mean-field approximation, the pbe has proved to be a very useful model of such electrostatics. however, numerically solving the pbe in a very efficient and accurate way is challenging. i will first describe the method and present some of my computational results. i will then compare different numerical methods for solving the pbe with complicated geometry. in particular, i will present the newly developed fast multipole method for the boundary integral discretization of the pbe. i will finally mentions some open questions. the results presented in talk are mainly from the work done in mccammon's group at ucsd.