Ricci solitons are important in the study of the Ricci flow and it plays a direct role as singularity dilations in the Ricci flow in 3 dimension. Under certain curvature assumptions, Perelman classified 3 dimensional gradient shrinking solitons. I would like to present some results on 4 dimensional gradient shrinking solitons by Ni-Wallach and Naber which extend Perelman's results to the 4 dimensional case.