We consider Ricci flows admitting closed and smooth tangent flows in the sense of Bamler 20. The tangent flow in question can be either a tangent flow at infinity for an ancient Ricci flow, or a tangent flow at a singular point for a Ricci flow developing a finite-time singularity. In these cases, we show that the tangent flow is unique and the singularity is of Type I. This talk is based on a joint work with Zilu Ma and Yongjia Zhang.