We present work toward the development of Model Order Reduction (MOR) techniques for fluid problems. As observed by several authors, CFD problems are particularly challenging for current MOR techniques due to the unavailability of low-dimensional linear approximation spaces for the solution manifold, and due to the fragility of standard Galerkin projection techniques for long-time integration. In this talk, we present two contributions to MOR: first, a nonlinear data compression technique based on a nonlinear mapping procedure; second, a constrained Galerkin formulation. The first contribution is designed to tackle problems with a slow-decaying Kolmogorov N-width by recasting the problem in a form that is more amenable for linear approximation spaces. The latter is designed to improve performance of Galerkin ROMs for long time integration of turbulent flows.