In this talk, we present staggered discontinuous Galerkin methods of arbitrary polynomial orders for the stationary Navier-Stokes equations on polygonal meshes. The exact divergence-free condition for the velocity is satisfied thanks to the carefully designed finite element spaces. The resulting method is pressure-robust so that the pressure approximation does not influence the velocity approximation, which is highly appreciated from a practical point of view. An edge-wise stabilization is proposed for the nonlinear convective term, which preserves the non-negativity. The optimal convergence estimates for all the variables in the L2 norm are proved. For a small enough rotational force, the velocity error is independent of the Reynolds number and of the pressure. Superconvergence can be achieved for the velocity error under a suitable projection. Numerical experiments are provided to validate the theoretical findings and demonstrate the performance of the proposed method. This is a joint work with Dohyun Kim, Eun-jae Park and Lina Zhao. The research is partially supported by the Hong Kong RGC General Research Fund (Projects: 14305624 and 14305423).