Abstract: The isoperimetric problem in spaces (both smooth and non-smooth) with a certain lower bound on the Ricci curvature has been solved in increasing generality with different approaches, in both the compact and non-compact setting.  In the non-compact setting, the classical isoperimetric inequality was generalized to the class of manifolds with non-negative Ricci curvature, coupled with a constraint on the volume growth of large balls (the Euclidean volume growth).  The equality case was characterized as well. The irreversibilty of Finsler manifold (i.e., the fact that the induced distance is not symmetric) severely harms the isoperimetric problem: most well-known isoperimetric inequalities valid for Riemannian manifolds do not have an analogous counterpart for irreversible Finsler manifolds, or their counterpart is not sharp.  The characterization of the equality case is far from being reached. In this talk, I will present a sharp isoperimetric inequality for possibly irreversible Finsler manifolds with non-negative Ricci curvature, having Euclidean volume growth.  I will also characterize the equality case and present an application to the weighted anisotropic isoperimetric problem in Euclidean cones.