The scale invariant solutions play an important role in understanding the singularity and asymptotic behavior of solutions for Navier-Stokes system. In this talk, we will discuss the recent progress on rigidity of steady solutions of Navier-Stokes system with scale invariant bounds, the existence of steady self-similar solutions when dimension is less than 17, and existence of two-dimensional forward self-similar solutions of Navier-Stokes system.