I will present the so-called "a-contraction with shifts” method, which is basically energy based. This method is quite useful in studying the stability of Riemann solution containing a shock under physically admissible perturbations. First, based on the method, we prove the long-time behavior of compressible Navier-Stokes flows perturbed from Riemann solution composed of a shock and other waves of different kinds. This resolves the long-standing problem since the 1980s. On the other hand, since the method can handle large perturbations of a shock, we can also prove the uniform stability of a shock w.r.t. the strength of viscosity, which provides the result on uniqueness of Riemann solution composed of a shock in the class of inviscid limits of solutions to the compressible Navier-Stokes system.