We say an n-dimensional Riemannian manifold is an m-Quasi Einstein metric if it is the base of an (n+m)-dimensional warped product Einstein manifold. We view the m-Quasi Einstein equation as a generalization of the Einstein equation (since an Einstein manifold is the base of a trivial product Einstein manifold). The m-Quasi Einstein equation is also closely related to the gradient Ricci soliton equation. In this talk I will discuss conditions on curvature/symmetry under which we can classify m-quasi Einstein metrics. This is joint work with Peter Petersen and Chenxu He.