Ricci flow deforms the Riemannian structure of a manifold in the direction of its Ricci curvature and tends to regularize the metric. This provides useful information about the underlying space. Ricci solitons are special solutions to the Ricci flow and arise naturally in the singularity analysis of the flow. We shall discuss some curvature and entropy gap theorems of gradient Ricci solitons. This talk is based on joint works with Yongjia Zhang and Zilu Ma, Eric Chen and Man-Chun Lee.