We review and discuss some of our recent numerical studies focusing on modeling synthetic jet actuators in selected high-fidelity numerical simulations targeting active flow, noise and icing control analyses. General aspects of the unsteady active flow control (AFC) using synthetic-jet actuation are first addressed, including integrating multiple design and analysis tools to account for various geometry and unsteady flow parameters. A numerical example is provided to illustrate high-accuracy numerical simulations of SJA-based AFC in application to low-Re airfoil unsteady aerodynamic response control, where a numerically efficient approach is developed to allow for the natural interaction of the generated synthetic jet with the external flow without the need to model the entire actuator dynamics. Such methodology is then applied to the selected application studies.