This monograph presents new constructive design methods for boundary stabilization and boundary estimation for several classes of benchmark problems in flow control, with potential applications to turbulence control, weather forecasting, and plasma control. The basis of the approach used in the work is the recently developed continuous backstepping method for parabolic partial differential equations, expanding the applicability of boundary controllers for flow systems from low Reynolds numbers to high Reynolds number conditions. Specific topics and features include an introduction of control and state estimation designs for flows that include thermal convection and electric conductivity; application of a special 'backstepping' approach where the boundary control design is combined with a particular Volterra transformation of the flow variables; unprecedented results for closed-form expressions for the solutions of linearized NavierStokes equations under feedback; and extension of the backstepping approach to eliminate one of the well-recognized root causes of transition to turbulence: the decoupling of the OrrSommerfeld and Squire systems. Control of Turbulent and Magnetohydrodynamic Channel Flows is an excellent reference for a broad, interdisciplinary engineering and mathematics audience: control theorists, fluid mechanicists, mechanical engineers, aerospace engineers, chemical engineers, electrical engineers, applied mathematicians, as well as research and graduate students in the above areas. The book may also be used as a supplementary text for graduate courses on control of distributed-parameter systems and on flow control.