\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.