Suppose (M, g) is an n-dimensional noncompact Riemannian manifold with nonnegative Ricci curvature, and let hk(M) be the dimension of the space of harmonic functions with polynomial growth of growth order at most k. In this talk, I will first review the previous works in estimating hk(M), then I will introduce my recent results on hk(M) in the case that M has maximal volume growth and the tangent cone at infinity of M is unique.