\indent the allen-cahn equation is a popular pde model for phase transition and phase separation. the level sets of solutions represent interfaces between two materials. a fine analysis of interfaces relies on solutions of allen-cahn equation in the entire spaces. in this talk, i will give a brief survey on results for local minimizers of the related allen-cahn energy functional, in particular in connection with the de giorgi conjecture which relates the level set of monotone solutions to minimal surfaces. i will further discuss a classification scheme for finite morse index solutions of allen-cahn equation in the whole plane. the level sets of such solutions may represent intersecting interfaces, and the energy of such solutions displays a quantization effect. in particular, i will show that saddle solutions must have even symmetry.