In this talk, we focus on the propagation of uniform (w.r.t the Mach number $varepsilon$ ) high order regularity and the incompressible limit for compressible Navier-Stokes equations in a domain with fixed or free boundaries. In the case of the fixed domain, we can establish the above results by assuming the initial data to be ill-prepared (in the sense that the acoustic part of the system is of order one initially). The simultaneous appearance of the boundary layers and the fast oscillation effects serves as the main obstacle of the proof. In the case of a domain with free boundaries, due to the extra difficulties arising from the regularity of the surface, we allow the data to be slightly well-prepared (in the sense that the acoustic part is at of order sqrt{varepsilon}). These are joint works with Professors Nader Masmoudi and Frederic Rousset.