In the talk I will first show a L2-contraction (a L2-type stability) of large viscous shock waves for the multi-dimensional scalar viscous conservation laws, up to a suitable shift by using the relative entropy methods. Quite different from the previous well-known results, we find a new way to determine the shift function, which depends both on the time and space variables and solves a viscous Hamilton-Jacobi type equation with source terms. Moreover, we do not impose any conditions on the anti-derivative variables of the perturbation around the shock profile. Then I will show our recent progress on the time-asymptotic stability of planar rarefaction wave to the multi-dimensional viscous conservation laws, such as compressible Navier-Stokes equations, Boltzmann equation and fluid-particle coupled system.