In this talk I will present some recent results obtained in collaboration with G. Carron and D. Tewodrose about the structure of Gromov-Hausdorff limits of manifolds with Ricci curvature satisfying a Kato integral bound. This condition is implied for instance by a lower Ricci curvature bound, or an integral Ricci bound in the spirit of the work of Petersen-Wei. We focus in particular on the introduction of new almost monotone quantities based on the heat kernel, and their role in proving a regularity theory that recovers previous results by Cheeger and Colding.