In the 1980s, Richard Hamilton invented the Ricci flow and initiated the geometric-analytic approach towards the Poincar\'e conjecture, which was eventually solved by Grisha Perelman. In this talk, we will briefly discuss the formation of singularities in the Ricci flow and the relations with Ricci solitons. We will introduce some recent advances and main conjectures in Ricci solitons, especially in steady gradient Ricci solitons. We end the talk by discussing some recent results (joint work with Professor Chow and Yuxing Deng) about asymptotic behaviors and a rigidity theorem of steady solitons.