We review the treatment of electrostatic interactions in computer simulations under periodic boundary conditions, with emphasis on Ewald summation. Connections between Ewald summation and reaction field approaches will be made within a unifying picture of electrostatic potentials in Wigner lattices. The calculation of thermodynamic pressures in simulations of polar and ionic media will be discussed. Effects of finite system size on charging free energies will be analyzed. In addition, we will briefly review the problem of defining proper thermodynamic limits for single-ion properties. We find that cluster (or droplet) calculations of ionic solvation enthalpies or free energies (e.g., based on quantum mechanical methods) contain a contribution stemming from the charge ordering in the cluster-vacuum interface. This interfacial potential can lead to deviations of calculated single-ion enthalpies and free energies from the values in a properly defined thermodynamic limit at infinite ionic dilution. Finally, we will study the validity of linear response approximations for Coulomb systems. The origin of non-linearities in charging free energies will be traced to variations in the microscopic structure. We will conclude with a discussion of accurate integration methods for non-linear free energy expressions. ©2000 American Institute of Physics.