  In this paper, we explore the limit structure of a sequence of Riemannian
manifolds with Bakry-\'Emery Ricci curvature bounded below in the
Gromov-Hausdorff topology. By extending the techniques established by
Cheeger-Cloding for Riemannian manifolds with Ricci curvature bounded below, we
prove that each tangent space at a point of the limit space is a metric cone.
We also analyze the singular structure of the limit space analogous to a work
of Cheeger-Colding-Tian. Our results will be applied to study the limit space
of a sequence of K\"ahler metrics arising from solutions of certain complex
Monge-Amp\`ere equations for the existence of K\"ahler-Ricci solitons on a Fano
manifold via the continuity method.
