The theory of Cherenkov and cyclotron plasma sources of coherent microwave radiation excited by intense electron beams is reviewed systematically. The linear approximation of the theory yields the output frequency spectra, the wave growth rates, and the threshold electron beam currents required for exciting these sources. The general theory is illustrated for some particular devices: the forward-wave plasma Cherenkov source, foward-and backward-wave cyclotron-resonance masers, and foward-and backward-wave Cherenkov sources in a slightly corrugated slow-wave structure. The nonlinear theory of plasma microwave sources leans heavily on a numerical solution of the dynamic equations of the electromagnetic field and the charged particles in the system. The nonlinear operation of a forward-wave plasma Cherenkov source is analyzed. Under optimum conditions, the efficiency of this device can reach 30--35\%. The efficiencies of other high-current plasma sources are comparable in magnitude. Experimental progress toward the development of high-power pulsed microwave sources of the Cherenkov and cyclotron types using intense relativistic electron beams is reviewed briefly.