Ricci flow is proved to be a powerful tool in the field of differential geometry. To obtain geometric or topological applications via continuing the Ricci flow by surgeries, it is of central importance to understand at least qualitatively the (finite-time) singularity models. In this talk, we present some recent developments mainly regarding the qualitative descriptions of the singularity models. We present two notions of blow-downs and their relations. We show an optimal scalar curvature estimate for singularity models. We then introduce some optimal qualitative and asymptotic descriptions for steady Ricci solitons, which are self-similar solutions of the Ricci flow and may arise as singularity models.