Electrostatic interactions are fundamental in colloidal and biological systems. Continuum models, such as the classical Poisson-Boltzmann (PB) theory, are efficient descriptions of such interactions. It is known, however, such a theory is unable to capture many important properties, such as the ionic size effect and charge-charge correlation. In this talk, I will first report some recent progress in developing mathematically PB-like continuum theories that account for additional electrostatic properties. I will then present a variational implicit-solvent model for biological molecules (such as proteins) in which the electrostatics is described through the dielectric boundary that separates a biomolecule from the surrounding solvent (i.e., water). I will show how the dielectric boundary force can be obtained as the shape derivative of the electrostatic free energy, and prove that such force can lead to an interfacial instability that has been observed in experiment and molecular dynamics simulations. Speaker(s): Bo Li (University of California, San Diego)