  The Poisson-Boltzmann (PB) theory is one of the most important theoretical
models describing charged systems continuously. However, it suffers from
neglecting ion correlations, which hinders its applicability to more general
charged systems other than extremely dilute ones. Therefore, some modified
versions of the PB theory are developed to effectively include ion
correlations. Focused on their applications to ionic solutions, the original PB
theory and its variances, including the field-theoretic approach, the
correlation-enhanced PB model, the Outhwaite-Bhuiyan modified PB theory and the
mean field theories, are briefly reviewed in this paper with the diagnosis of
their advantages and limitations.
