Suppose (M, g) is an n-dimensional noncompact Riemannian manifold with nonnegative Ricci curvature, and let h k(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 h k(M), then I will introduce my recent results on h k(M) in the case that M has maximal volume growth and the tangent cone at infinity of M is unique.