The objective of this dissertation is to develop open and closed-loop control algorithms for manipulating wake flows past a solid cylinder in an electrically low-conducting fluid (e.g. seawater). The intent is to avoid both vortex shedding and flow separation from the body. It is desired to reduce the mean drag significantly and prevent the lift from becoming non-zero at all times. This is achieved through the introduction of a Lorentz force in the azimuthal direction generated by an array of permanent magnets and electrodes located on the solid structure. The array of actuators offers the advantage of making the Lorentz force time and space dependent. More specifically, a closed-loop control algorithm has been derived from the equations of motion capable of determining at all times the intensity of the Lorentz force in order to control the flow. This is achieved first, independently of the flow (open loop algorithm) and second, based on some partial flow information measured on the surface of the solid body (closed-loop algorithm). The latter offers the advantage of requiring a significantly reduced amount of control power. After considering the flow past a fixed solid structure, there is control of the more complex flowstructure interaction that occurs when the body is free to move. Thus it is possible to prevent any flow induced vibration from occurring.