The Poisson and Poisson-Boltzmann Eqs. are extremely useful for a quantitative description of electrostatic effects in molecules, macromolecules, and more macroscopic systems. Real-space grid methods prove effective for solving these types of equations for general macroion charge distributions, shapes and solution ionic strengths. In the case of a mobile Coulomb gas (e.g., simple ions in solution) surrounding fixed macroion charge distributions, the thermodynamics of the system is simply related to the PB field. Generalization of the PB Eq. to treat more complicated systems (e.g., mobile dipoles, finite size simple ions) can be accomplished via the Lattice Field Theory formulation of the appropriate statistical mechanical problem.