We will present a general methodology to derive well-posed boundary integral equations for frequency domain scattering problems. The methodology relies on use of coercive approximations of Dirichlet-to-Neumann maps. The resulting integral equations have excellent spectral properties throughout the frequency spectrum for both scalar and vector scattering problems and all kinds of boundary conditions (Dirichlet, Neumann, transmission, PEC). The rate of convergence of our high-order solvers based on these boundary integral operators is almost independent of frequency for non-trapping scatterers. Joint work with: Y. Boubendir (NJIT), O. Bruno (Caltech), V. Dominguez (Navarra, Spain), and D. Levadoux (ONERA, France).