Superconductors, Bose-Einstein condensates and liquid crystals are belong to condense matters with many investigations in physics and chemistry. Nonlinear PDE (partial differential equation) models like Ginzburg-Landau, Gross-Pitaevskii and Landau-de Gennes equations are mathematical models of these condense matters. Analysis of nonlinear elliptic equations plays an important role on the study of Ginzburg-Landau equations for (point) vortices of superconductors, Gross-Pitaevskii equations for domain walls of Bose-Einstein condensates, and Landau-de Gennes equations for biaxial (line) defects of liquid crystals. In this lecture, I shall survey techniques of variational method to study these PDE models and introduce some open problems related to these PDE models.