Steady ricci solitons are important examples of singularities models. In higher dimensions, singlarity models can be steady Ricci solitons on orbifolds. In this talk, we will review some rigidity theorems on positively curved steady ricci solitons on manifolds. We will also classify noncollapsed steady ricci solitons on orbifolds with compact singularity of codimension 2, positive curvature operator and linear curvature decay.