  This review describes the theory and implementation of implicit solvation
models based on continuum electrostatics. Within quantum chemistry this
formalism is sometimes synonymous with the polarizable continuum model, a
particular boundary-element approach to the problem defined by the Poisson or
Poisson-Boltzmann equation, but that moniker belies the diversity of available
methods. This work reviews the current state-of-the art, with emphasis on
theory and methods rather than applications. The basics of continuum
electrostatics are described, including the nonequilibrium polarization
response upon excitation or ionization of the solute. Nonelectrostatic
interactions, which must be included in the model in order to obtain accurate
solvation energies, are described as well. Numerical techniques for
implementing the equations are discussed, including linear-scaling algorithms
that can be used in classical or mixed quantum/classical biomolecular
electrostatics calculations. Anisotropic models that can describe interfacial
solvation are briefly described.
