introduced by hamilton about thirty-five years ago, ricci flow has developed into an integral and vital part of the geometric analysis. some of its spectacular successes include the resolution of the poincare conjecture for three manifolds and the complete classification of quarter pinched riemannian manifolds. ricci solitons, as self-similar solutions to ricci flow, play an important role in understanding the singularity formation and long time dynamics of the flow. the talk will focus on the so-called shrinking solitons. we will review their classification in dimension two and three case, and mention some recent progress made jointly with ovidiu munteanu concerning their geometry in dimension four.