Understanding biomolecules---their structures, dynamics, and interactions with solvent---is essential to revealing mechanisms and functions of biological systems. While atomistic simulations that treat both solvent and solute molecules explicitly are usually more accurate, implicit or continuum solvent models for biomolecules are far more efficient. With an implicit solvent, the free energy and structure of an underlying solvation system is described through the solute particles and the interface that separates the solutes and solvent. Dzubiella, Swanson and McCammon [Phys. Rev. Lett.104, 527 (2006) and J. Chem. Phys. 124, 084905 (2006)] developed a class of variational implicit-solvent models. Central in these models is a free-energy functional of all admissible solute-solvent interfaces, coupling both nonpolar and polar contributions of an underlying system. An energy-minimizing interface then defines an equilibrium solute-solvent interface. Cheng et al. [J. Chem. Phys. 127, 084503 (2007)] developed a robust level-set method for numerically capturing such interfaces. In this talk, I will give an overview of the recent development of variational implicit-solvent approach for solvation systems. I will point out how various kinds of mathematical concepts and techniques from differential geometry and partial differential equations can be applied to this approach. Joint work with Jianwei Che, Li-Tien Cheng, Joachim Dzubiella, J. Andy McCammon, and Yang Xie.