The talk gives an introduction to the method for the calculation of electrostatic interactions put forward by Maggs, both in its Monte Carlo and in its Molecular Dynamics version. It is shown that the latter can be viewed as a straightforward application of the Car-Parrinello approach to the coupled dynamics of charges and electromagnetic fields, which is equivalent to a Galilei-invariant form of Maxwell theory. The talk then focuses on more recent developments, where the same idea is applied to solving the Poisson-Boltzmann equation. It is shown that the resulting algorithm is rather simple and intrinsically stable.