Abstract: Gauss curvature flow was used to model the tumbling of the stones. In applied sciences the flow by the power of the Gauss curvature was also proposed. The long time existence of this flow was studied by various people including Tso, Chow, Andrews etc. Recently progresses were made in understanding the asymptotic behavior. I shall discuss the joint work with Andrews and Guan, which together with the recent work of Brendle, Choi, Daskalopulos settles the Firey’s conjecture as a special case.