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The focus of this work is on theoretical analysis of fundamental aspects of high-speed flow control using electric and magnetic fields. The principal challenge is that the relatively cold gas is weakly ionized in electric discharges or by electron beams, with ionization fraction ranging from 10 −8 to 10 −5 . The low ionization fraction means that, although electrons and ions can interact with electromagnetic fields, transfer of momentum and energy to or from the bulk neutral gas can be quite inefficient. Analytical estimates show that, even at the highest values of the electric field that can exist in cathode sheaths of electric discharges, electrohydrodynamic, or ion wind, effects in a single discharge can be of significance only in low-speed core flows or in laminar sublayers of high-speed flows. Use of multi-element discharges would amplify the single-sheath effect, so that the cumulative action on the flow can conceivably be made significant. However, Joule heating can overshadow the cathode sheath ion wind effects. Theoretical analysis of magnetohydrodynamic (MHD) flow control with electron beam ionization of hypersonic flow shows that the MHD interaction parameter is a steeply increasing function of magnetic field strength and the flow velocity. However, constraints imposed by arcing between electrode segments can reduce the performance and make the maximum interaction parameter virtually independent of Mach number. Estimates also show that the MHD interaction parameter is much higher near the wall (in the boundary layer) than in the core flow, which may have implications for MHD boundary layer and transition control. The paper also considers “electrodeless” MHD turning and compression of high-speed flows. Computations of a sample case demonstrate that the turning and compression of hypersonic flow ionized by electron beams can be achieved; however, the effect is relatively modest due to low ionization level.