Computational fluid dynamics (CFD) can be employed for investigating the relevant physical mechanisms associated with active flow control (AFC). High fidelity simulations provide insight into why particular AFC applications are effective and efficient. The paper starts out with a categorization of different CFD approaches according to the flow properties and available computer resources. Then, several examples of research from our CFD laboratory are presented where we successfully employed CFD for investigating AFC techniques. These examples demonstrate the capabilities and limitations of CFD when investigating AFC. For example, Reynolds-averaged Navier-Stokes may be employed for investigating steady flow control (such as a high Reynolds number Coanda wall jet for circulation control). For unsteady flow control (such as separation control by pulsed vortex generator jets) the flow structures that are relevant for the effectiveness of the actuation have to be resolved.