Abstract: The vanishing-viscosity limit studies the behavior of solutions to the Navier-Stokes equations as the viscosity parameter approaches zero. In the presence of a physical boundary, it remains largely an open question whether solutions of the Navier-Stokes equations with low viscosity (or high Reynolds number) approximate a solution of the Euler equations. In this talk, we review our recent results on the vanishing-viscosity limit of the 3D Navier-Stokes equations with Navier boundary conditions in the half-space. We begin by introducing the mathematical framework of our work, which consists of L^2-based Sobolev conormal spaces, and discussing key assumptions. Next, we highlight some challenges and explain how our findings establish a new functional setting in which the Euler equations are well-posed. Finally, we comment on the challenges in the L^p case and explain how to obtain convergence. This is joint work with Igor Kukavica.