This talk represents joint work with Aaron Naber (who will give a closely related talk on harmonic maps and minimal hypersurfaces). Let Y^n denote the Gromov-Hausdorff limit of a sequence of Riemannian manifolds M_i^n with Ricci curvature >= -(n-1) and Vol(B_1(m_i)) >= v>0, for all m_i in M_i^n. For all y in Y^n, every tangent cone Y_y is a metric cone. The stratification S_0 ⊂ S_1 ⊂ ... ⊂ S_(n-2) off the singular set S is defined by: y is in S_k if no Y_y splits off a factor R^(k+1) isometrically. It is known that dim(S_k)