  Modeling of biomolecular systems plays an essential role in understanding
biological processes, such as ionic flow across channels, protein modification
or interaction, and cell signaling. The continuum model described by the
Poisson-Boltzmann (PB)/Poisson-Nernst-Planck (PNP) equations has made great
contributions towards simulation of these processes. However, the model has
shortcomings in its commonly used form and cannot capture (or cannot accurately
capture) some important physical properties of biological systems. Considerable
efforts have been made to improve the continuum model to account for discrete
particle interactions and to make progress in numerical methods to provide
accurate and efficient simulation. This review will summarize recent main
improvements in continuum modeling for biomolecular systems, with focus on the
size-modified models, the coupling of the classical density functional theory
and PNP equations, the coupling of polar and nonpolar interactions, and
numerical progress.
