Since the work of De Lellis and Szekelyhidi on the non-uniqueness of solutions to the incompressible Euler system, a lot of work has been done to understand whether, into some certain regime, these spurious solutions can be discarded. In the compressible case, De Lellis, Kreml, and Chiodaroli, showed that, in dimension bigger or equal than 2, steady planar shocks solutions are also not unique. One hope to recover uniqueness, is to consider only functions which can be constructed as inviscid limits of solutions to Navier- Stokes equations. Surprisingly, even in 1D, the question of uniqueness is still open (at least without assuming small BV initial values, or artificial a priori estimates). In this talk, we will show that 1D entropic shocks are stable (and so unique) in a class of vanishing viscosity limits of compressible Navier-Stokes equations. The result holds without any regularity constraint on the initial values of the perturbations. The result is based on a strong stability result for viscous shocks, which is uniform with respect to the viscosity. It is strongly related to the notion of a-contraction, first introduced by the authors, for the study of the stability of inviscid shocks for conservation laws. This is a joint project with Professor Kang Moon-Jin.