Let $(M,g)$ be a smooth, complete Riemannian manifold with nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay which is not isometric to $\mathbb{R}^n$. I will discuss joint work with Gioacchino Antonelli and Marco Pozzetta where we prove that there exists a set $\mathcal{G}\subset (0,\infty)$ with density one at infinity such that for each volume $V\in\mathcal{G}$ there is a unique isoperimetric region with volume $V$ inside $M$.