Chaotic fluctuations in wake flows can degrade aerodynamic system performance and generate aerodynamic noise. To address these challenges, we employ a resolvent-based approach to estimate and mitigate flow perturbations. Our estimators and controllers are built using two approaches: 1) an operator-based approach that offers low computational cost without requiring a priori model reduction and incorporates colored statistics that represent the nonlinear terms of the Navier-Stokes equations, and 2) a data-driven approach that avoids the need to construct linearized Navier-Stokes operators and naturally incorporates the colored statistics of the nonlinear terms. The Wiener-Hopf method is used to ensure optimal causality in the estimator and controller. Using NEK5000, we demonstrate effective estimation and control of downstream fluctuations in transitional flow over a backward-facing step. We then implement our tools within the compressible flow solver CharLES and demonstrate the effectiveness of estimation and control in both laminar and turbulent flows over a NACA 0012 airfoil.