  In this article, we provide some volume growth estimates for complete
noncompact gradient Ricci solitons and quasi-Einstein manifolds similar to the
classical results by Bishop, Calabi and Yau for complete Riemannian manifolds
with nonnegative Ricci curvature. We prove a sharp volume growth estimate for
complete noncompact gradient shrinking Ricci soliton. Moreover, we provide
upper bound volume growth estimates for complete noncompact quasi-Einstein
manifolds with $\lambda=0.$ In addition, we prove that geodesic balls of
complete noncompact quasi-Einstein manifolds with $\lambda<0$ and $\mu\leq 0$
have at most exponential volume growth.
