In this talk, I will present the results of a joint paper of Jeong Hyeong Park and myself in which we give a classification of Einstein hypersurfaces in irreducible symmetric spaces. The main theorem states that there are three classes of such hypersurfaces, belonging to three different geometries: homogeneous geometry (for Einstein hypersurfaces in noncompact symmetric spaces), Legendrian geometry (Einstein hypersurfaces in SU(3)/SO(3) and affine geometry (Einstein hypersurfaces in SL(3)/SO(3)).