The talk is concerned with our recent results on the vanishing viscosity limit of planar rarefaction wave to both 2D compressible isentropic Navier-Stokes equations and 3D full compressible Navier-Stokes equations and the zero dissipation limit of planar contact discontinuity of 3D full compressible Navier-Stokes equations, which, in particular, impies the uniqueness of a planar contact discontinuity for 3D compressible Euler equations in the class of zero dissipation limit of compressible Navier-Stokes equations.