I will discuss the stability of the Couette flow in dimension 3 for the Navier-Stokes equations. For a given viscosity, the question is to find the maximal size of perturbations for which the flow goes back to the Couette flow. I will present results in Sobolev, and in Gevrey regularity. In the latter case, we can construct solutions which grow from arbitrarily small to a size O(1), before going back to Couette. They can be thought of as the boundary of the basin of attraction. This is joint work with Jacob Bedrossian and Nader Masmoudi.